Saving cutout to jpg

Hi all

when I have opened a photo/image in Photoshop cs2 then unlocked the layer,removed part of the background making it a cutout. Should I be able to save the layer (cutout) in the jpg format. When I save in jpg the white background which I have deleted returns. I seem only to be able to save to psd format to be able to save with no backgroud.I seem sure I have saved to jpg when doing the same sort of thing in the past.
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Regards anthonyq