Randomize lines in two files, keeping relative order

I recently wanted to randomize the lines in two files, but to keep the relative order of the lines between the files. So I can remember how to do this next time I will post it here.

for i in `cat file1.txt`;do echo $RANDOM;done >randomOrder.txt
paste randomOrder.txt  file1.txt file2.txt  |sort -k1n >sorted.txt
cut -f 2 sorted.txt  >file1.txt
cut -f 3 sorted.txt  >file2.txt
rm -f sorted.txt
rm -f randomOrder.txt