The NY Trans Fat Ban

Plenty of criticism has already been made regarding the ban on trans fat just passed by New York city. Should the government really be micromanaging people's lives in this way? Are the alternatives that will be used any healthier? But an additional concern just struck me. Reading the NY Times piece on the ban, I came across this sentence:

New York’s Board of Health, made up mostly of physicians and health professionals appointed by the mayor, can adopt regulations without approval by any other agency.

Really? A group of unelected public officals can establish these regulations entirely on their own? Maybe there's something more to the process than I'm aware of, but if the Times' description is accurate, that seems like a bad way to make laws.