Need help with basename command

I have a file

fileinput.txt:

File home/me/fileA.doc is size 232
File home/you/you/fileB.doc is size 343
File /directory/fileC.doc is size 433
File /directory/filed.doc cannot find file size

I want to use the basename command (or any other command) to output:

File fileA.doc is size 232
File fileB.doc is size 343
File fileC.doc is size 433
File filed.doc cannot find file size

I've tried:

/usr/bin/nawk � file=$0
            Basename $file � fileinput.txt 

But that just prints out the original file! Any suggestions?

cat  fileinput.txt | awk -F/ '{print $NF}'
awk '{sub(/.*\//,"",$2)}1' infile
sed 's#[^ \t]*/##g' infile

Parameter substitution might work as well here.

Mike