NEW YORK, July 23 (Reuters) - Hudson City Bancorp Inc (HCBK.O: Quote, Profile, Research), which runs one of New Jersey's largest banks, said on Wednesday second-quarter profit increased 52 percent, helped by an improved net interest margin as it lowered deposit rates even as mortgage yields stayed stable.

Net income for the Paramus-based parent of Hudson City Savings Bank rose to $110.7 million, or 22 cents per share, from $72.7 million, or 14 cents, a year earlier. (Reporting by Jonathan Stempel; Editing by Dave Zimmerman)