it's a bit irritating that fresh fund rates are sooo much higher than other rates

thinking of doing this:
1) I have an existing 10k fixed deposit at bank 1 (1 month tenure)
2) place 10k fresh funds at bank 1 and get higher rate for new fixed deposit (6 months tenure)
3) a bit later uplift my existing fixed deposit at bank 1 and move it to another bank 2 to get higher rate there

will this work?