I tried this:

#!/usr/bin/perl 

use strict;
use warnings;

$|=1;

use Sys::RunAlone;

print "Script $0 is running now.\n";
die "Another $0 is already running.\n"
    unless open my $self, '<', $0;
        
CheckRaceCondition();
sleep(5);
print "End.\n";

sub CheckRaceCondition {
    die "Another $0 is already running.\n"
        unless open $self, '<', $0;  
}

__END__
[download]

For an in-depth discussion of Fcntl and flock see:

Ensuring only one copy of a perl script is running.

Then, for a great solution to the problem by ikegami, see:

Re^2: Ensuring only one copy of a perl script is running