Getting the most current(date-wise) record from mysql database

Hi

My mysql datatbase has row entries with two column headers :-name_of_file and date_modified.
Example:
name_of_file  date_modified
pooh.txt         2004-12-04
piglet.txt        2005-01-03
pooh.txt        2005-01-01

Note that pooh.txt is the same file but we have two row entries for it. This is because everytime we modify the file , there is an entry for it in the database with the modified date.

Is there a way i can select rows such that if a file appears more than once, i can select the row containing the most "up-to-date"/recent date?

For example, how can I get the output below?
name_of_file  date_modified
piglet.txt        2005-01-03
pooh.txt        2005-01-01 (We ignored "pooh.txt   2004-12-04" as the date 2005-01-01 is more recent than 2004-12-04)