Here's one way to do it, by simply chomping the line ending from every other line:

#!perl -i.bak

$toggle = 0;

while (<>) {
  chomp if $toggle ^= 1;
  print;
}

print "\n" if $toggle;    # if the last line was chomped
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If you wanted, you could use the -p option to make the reading and printing parts automatic:

#!perl -pi.bak

BEGIN { $toggle = 0; }

chomp if $toggle ^= 1;

END { print "\n" if $toggle; }
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