As japhy suggests, the Fisher-Yates shuffle is a good solution. If you want to save yourself the trouble of coding it, I've got it implemented in Math::NumberCruncher. Math::NumberCruncher also has numerous other similar functions that may be useful. Using Math::NumberCruncher, you could do the above like so:

use strict;
use Math::NumberCruncher;

my @chars = ( 'A' .. 'Z' );

my $ref = Math::NumberCruncher->new();

$ref->ShuffleArray( \@chars );

foreach my $char ( @chars ) {
    print $char, "\n";
}
[download]

UPDATE: Pursuant to Juerd's post, in the interest of TMTOWTDI, here's the code using Math::NumberCruncher through its original functional interface:

use strict;
use Math::NumberCruncher;

my @chars = ( 'A' .. 'Z' );
Math::NumberCruncher::ShuffleArray( \@chars );
foreach my $char ( @chars ) {
    print $char, "\n";
}
[download]

___________________
Kurt