On January 2, 2006, at 1152 eastern standard time, a Piper PA-28-161, N2759M, was substantially damaged while ditching in the Hudson River, following a total loss of engine power in cruise flight near Yonkers, New York. The certificated private pilot and flight instructor sustained minor injuries. Visual meteorological conditions prevailed for the instructional flight that departed South Jersey Regional Airport (VAY), Mount Holly, New Jersey; destined for Lincoln Park Airport (N07), Lincoln Park, New Jersey. No flight plan was filed for the instructional flight conducted under 14 CFR Part 91. The pilots stated that the flight instructor was familiarizing him with operating in the visual flight rules (VFR) corridor along the Hudson River. Prior to takeoff, the private pilot had the airplane completely fueled. The airplane was in cruise flight about 900 feet agl, traveling north over the river when without warning, the engine sputtered and lost all power near the George Washington Bridge. The pilots did not hear any mechanical binding, and the propeller continued to turn while the engine sputtered. The flight instructor transmitted a distress signal, and took control of the airplane. An attempt to restart the engine was unsuccessful, and the flight instructor ditched the airplane in the Hudson River. The New York City Police Department and United States Coast Guard subsequently rescued the pilots, and searched for the wreckage. As of the publication date of this report, the wreckage had not been located. The airplane underwent a 100-hour inspection on November 15, 2005. At that time, the airplane had accumulated 4,939 hours of operation. LaGuardia Airport (LGA), Flushing, New York, was located about 5 miles southeast of the accident site. The reported weather at LGA, at 1151, was: wind from 160 degrees at 7 knots; visibility 10 miles; few clouds at 12,000 feet; overcast ceiling at 15,000 feet; temperature 45 degrees F; dew point 30 degrees F; altimeter 30.20 inches Hg.