Cutting frozen steak

Hi all,

Today I bought a pound of steak which came to me frozen. I wondered what the best way to cut it would be since it’s one solid piece and I won’t eat a pound at once.

What I did was putting the steak with the wrapper in warm water so the first 5mm’s would defrost, then cut it into blocks and quickly put it in a new plastic (not vacuum ones) bag and put it in the freezer again.

Is this a good way or am I already doomed bacteria wise because the outer layer was defrosted?

Thanks!