In combinatorial mathematics, a derangement is a permutation of the elements of a set in which no element appears in its original position.
I unsuccessfully tried to find deranged couples of English words with Google, but it suddenly occurred to me to read my old blog post about anagrams and palindromes. There I wound the following couple:
R E P A P E R
P R E P A R E
Then I found several couples of deranged words in the Wikipedia text quoted above:
W O R D S N O F I X E D
S W O R D O N D E F I X
My take-home message to you, dear readers, is that searching the Web with Google is not always the fastest way to find something.