No, not at all, you have to pay up front for relisting - what happens is that if you relist something (but only for the first time of relisting) you'll see a message which says "you may be credited with your listing fee if it sells this time" (or something like that).
You'l get your money back if you sell it this time round (but not for a third relisting).
btw it's free listing on 100 items tomorrow and Sunday - then you CAN relist for free, as many times as you like - I often keep my unsold items back to relist them onver a free weekend.