The old way of avoiding "global" filehandles was:

local *FILEHANDLE;
open FILEHANDLE, ">$strFileName"
    or die "Couldn't open '$strFileName': $!";
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The new, and far better way of doing filehandles is the lexical way, and there are no disadvantages that spring to mind immediately, so you should be using the new way unless your platform requirements only allow for Perl 5.005 (default on Solaris 2.6) or Perl 5.004 (default on older Solaris I believe).