No, but banks will offer better terms to get additional deposits (so they can lend them and make money off the spread), then lower the rate somewhat once they've gotten what they can redeploy. They're hoping you'll be lazy and stay. So (a) be prepared for that, and (b) consider switching to a bank that has a reputation for being among the best for longer periods of time. If you do chase rates, be prepared to decide whether it's worth switching for a 0.5% difference (which, once you do the math and subtract taxes, is not that much money really).
Make sure it's FDIC insured, of course, and if you're concerned about that you can check with the FDIC themselves instead of the bank.