Substitute a string with itself!
CJam, 11 bytes

q__1m&gt;.{er}


Test it here.

Explanation

q__    e# Read input and make two copies.
1m&gt;    e# Rotate the second copy one character to the right.
.{er}  e# For each pair of characters from the second and third string,
       e# replace occurrences of the first with the second.