Keep a hash of $File entries you've seen. You'll have to mangle them to make sure that algiz and algiz-r use the same key, but that's pretty easy.

my %seen;

while (<FILE>)
{
    chomp;
    my ($file, $name, $keyword) = split( /:/, $_, 3 );

    (my $filekey = $file) =~ s/-r$//;
    next if $seen{$filekey}++;
    ($File[$i], $Name[$i], $Keywords[$i]) = ( $file, $name, $keyword )
+;
    $i++;
}
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