diff --git a/MagickCore/memory.c b/MagickCore/memory.c
index 6530ffee90..3beebfce62 100644
--- a/MagickCore/memory.c
+++ b/MagickCore/memory.c
@@ -1639,7 +1639,8 @@ MagickPrivate MagickBooleanType ShredMagickMemory(void *memory,
 
     for (j=0; j < length; j+=quantum)
     {
-      SetRandomKey(random_info,quantum,GetStringInfoDatum(key));
+      if (i != 0)
+        SetRandomKey(random_info,quantum,GetStringInfoDatum(key));
       (void) memcpy(p,GetStringInfoDatum(key),(size_t)
         MagickMin(quantum,length-j));
       p+=quantum;
diff --git a/MagickCore/utility.c b/MagickCore/utility.c
index 52f399c645..036cb36d01 100644
--- a/MagickCore/utility.c
+++ b/MagickCore/utility.c
@@ -1944,7 +1944,8 @@ MagickPrivate MagickBooleanType ShredFile(const char *path)
       break;
     for (j=0; j < (MagickOffsetType) length; j+=count)
     {
-      SetRandomKey(random_info,quantum,GetStringInfoDatum(key));
+      if (i != 0)
+        SetRandomKey(random_info,quantum,GetStringInfoDatum(key));
       count=write(file,GetStringInfoDatum(key),(size_t)
         MagickMin((MagickSizeType) quantum,length-j));
       if (count <= 0)