I most often use continue like this: I put the 'close ARGV if eof;' statement needed to reset $INPUT_LINE_NUMBER for each input filehandle (i.e., ARGV) in a continue block in the documented way:

use strict;
use warnings;

use English qw( -no_match_vars );

RECORD:
while (my $record = <>) {
    # Line number 1 is a header...
    if ($INPUT_LINE_NUMBER == 1) {
        # Per-file preprocessing goes here...

        next RECORD; # Skip to next record...
    }

    # Per-record processing goes here...
}
continue {
    close ARGV if eof;
}
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Jim