diff --git a/Source/cmSystemTools.cxx b/Source/cmSystemTools.cxx
index 4e1f9453e..f4ce41c78 100644
--- a/Source/cmSystemTools.cxx
+++ b/Source/cmSystemTools.cxx
@@ -26,6 +26,7 @@
 #if defined(CMAKE_BUILD_WITH_CMAKE)
 # include <cmsys/Terminal.h>
 #endif
+#include <cmsys/stl/algorithm>
 
 #if defined(_WIN32)
 # include <windows.h>
@@ -2478,54 +2479,87 @@ bool cmSystemTools::ChangeRPath(std::string const& file,
 bool cmSystemTools::RemoveRPath(std::string const& file, std::string* emsg)
 {
 #if defined(CMAKE_USE_ELF_PARSER)
-  unsigned long rpathPosition = 0;
-  unsigned long rpathSize = 0;
-  unsigned long rpathEntryPosition = 0;
+  int zeroCount = 0;
+  unsigned long zeroPosition[2] = {0,0};
+  unsigned long zeroSize[2] = {0,0};
+  unsigned long bytesBegin = 0;
   std::vector<char> bytes;
   {
   // Parse the ELF binary.
   cmELF elf(file.c_str());
 
-  // Get the RPATH or RUNPATH entry from it.
-  cmELF::StringEntry const* se = elf.GetRPath();
-  if(!se)
+  // Get the RPATH and RUNPATH entries from it and sort them by index
+  // in the dynamic section header.
+  int se_count = 0;
+  cmELF::StringEntry const* se[2] = {0, 0};
+  if(cmELF::StringEntry const* se_rpath = elf.GetRPath())
     {
-    se = elf.GetRunPath();
+    se[se_count++] = se_rpath;
+    }
+  if(cmELF::StringEntry const* se_runpath = elf.GetRunPath())
+    {
+    se[se_count++] = se_runpath;
+    }
+  if(se_count == 0)
+    {
+    // There is no RPATH or RUNPATH anyway.
+    return true;
+    }
+  if(se_count == 2 && se[1]->IndexInSection < se[0]->IndexInSection)
+    {
+    cmsys_stl::swap(se[0], se[1]);
     }
 
-  if(se)
+  // Get the size of the dynamic section header.
+  unsigned int count = elf.GetDynamicEntryCount();
+  if(count == 0)
     {
-    // Store information about the entry.
-    rpathPosition = se->Position;
-    rpathSize = se->Size;
-    rpathEntryPosition = elf.GetDynamicEntryPosition(se->IndexInSection);
-
-    // Get the file range containing the rest of the DYNAMIC table
-    // after the RPATH entry.
-    unsigned long nextEntryPosition =
-      elf.GetDynamicEntryPosition(se->IndexInSection+1);
-    unsigned int count = elf.GetDynamicEntryCount();
-    if(count == 0)
+    // This should happen only for invalid ELF files where a DT_NULL
+    // appears before the end of the table.
+    if(emsg)
       {
-      // This should happen only for invalid ELF files where a DT_NULL
-      // appears before the end of the table.
-      if(emsg)
-        {
-        *emsg = "DYNAMIC section contains a DT_NULL before the end.";
-        }
-      return false;
+      *emsg = "DYNAMIC section contains a DT_NULL before the end.";
       }
-    unsigned long nullEntryPosition = elf.GetDynamicEntryPosition(count);
+    return false;
+    }
 
-    // Allocate and fill a buffer with zeros.
-    bytes.resize(nullEntryPosition - rpathEntryPosition, 0);
+  // Save information about the string entries to be zeroed.
+  zeroCount = se_count;
+  for(int i=0; i < se_count; ++i)
+    {
+    zeroPosition[i] = se[i]->Position;
+    zeroSize[i] = se[i]->Size;
+    }
 
-    // Read the part of the DYNAMIC section header that will move.
-    // The remainder of the buffer will be left with zeros which
-    // represent a DT_NULL entry.
-    if(!elf.ReadBytes(nextEntryPosition,
-                      nullEntryPosition - nextEntryPosition,
-                      &bytes[0]))
+  // Get the range of file positions corresponding to each entry and
+  // the rest of the table after them.
+  unsigned long entryBegin[3] = {0,0,0};
+  unsigned long entryEnd[2] = {0,0};
+  for(int i=0; i < se_count; ++i)
+    {
+    entryBegin[i] = elf.GetDynamicEntryPosition(se[i]->IndexInSection);
+    entryEnd[i] = elf.GetDynamicEntryPosition(se[i]->IndexInSection+1);
+    }
+  entryBegin[se_count] = elf.GetDynamicEntryPosition(count);
+
+  // The data are to be written over the old table entries starting at
+  // the first one being removed.
+  bytesBegin = entryBegin[0];
+  unsigned long bytesEnd = entryBegin[se_count];
+
+  // Allocate a buffer to hold the part of the file to be written.
+  // Initialize it with zeros.
+  bytes.resize(bytesEnd - bytesBegin, 0);
+
+  // Read the part of the DYNAMIC section header that will move.
+  // The remainder of the buffer will be left with zeros which
+  // represent a DT_NULL entry.
+  char* data = &bytes[0];
+  for(int i=0; i < se_count; ++i)
+    {
+    // Read data between the entries being removed.
+    unsigned long sz = entryBegin[i+1] - entryEnd[i];
+    if(sz > 0 && !elf.ReadBytes(entryEnd[i], sz, data))
       {
       if(emsg)
         {
@@ -2533,11 +2567,7 @@ bool cmSystemTools::RemoveRPath(std::string const& file, std::string* emsg)
         }
       return false;
       }
-    }
-  else
-    {
-    // There is no RPATH or RUNPATH anyway.
-    return true;
+    data += sz;
     }
   }
 
@@ -2554,7 +2584,7 @@ bool cmSystemTools::RemoveRPath(std::string const& file, std::string* emsg)
     }
 
   // Write the new DYNAMIC table header.
-  if(!f.seekp(rpathEntryPosition))
+  if(!f.seekp(bytesBegin))
     {
     if(emsg)
       {
@@ -2571,33 +2601,33 @@ bool cmSystemTools::RemoveRPath(std::string const& file, std::string* emsg)
     return false;
     }
 
-  // Fill the RPATH string with zero bytes.
-  if(!f.seekp(rpathPosition))
+  // Fill the RPATH and RUNPATH strings with zero bytes.
+  for(int i=0; i < zeroCount; ++i)
     {
-    if(emsg)
+    if(!f.seekp(zeroPosition[i]))
       {
-      *emsg = "Error seeking to RPATH position.";
+      if(emsg)
+        {
+        *emsg = "Error seeking to RPATH position.";
+        }
+      return false;
+      }
+    for(unsigned long j=0; j < zeroSize[i]; ++j)
+      {
+      f << '\0';
+      }
+    if(!f)
+      {
+      if(emsg)
+        {
+        *emsg = "Error writing the empty rpath string to the file.";
+        }
+      return false;
       }
-    return false;
-    }
-  for(unsigned long i=0; i < rpathSize; ++i)
-    {
-    f << '\0';
     }
 
-  // Make sure everything was okay.
-  if(f)
-    {
-    return true;
-    }
-  else
-    {
-    if(emsg)
-      {
-      *emsg = "Error writing the empty rpath to the file.";
-      }
-    return false;
-    }
+  // Everything was updated successfully.
+  return true;
 #else
   (void)file;
   (void)emsg;