There are lots of ways to do it, and this thread will likely fill up with them. I can't help noticing that what you're looking for resembles the unix command "dirname", however.

chomp($str = `dirname $str`);
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Yes, it's silly and not portable. I'm just covering a base here. :-)

The dirname method in File::Basename would be a good choice if you are in fact manipulating directory paths. This module is reasonably platform independent and part of the core Perl distribution.

use File::Basename;

my $dir = dirname($filename);
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Do "perldoc File::Basename" for more information.