On March 10, 2010, about 1255 eastern standard time, A Gulfstream G1159A, N155MM, registered to N155MM LLC, operated by Northeastern Aviation Corporation, experienced a loss of engine power on the No. 2 engine while climbing through 35,000 feet mean sea level (msl). Visual meteorological conditions prevailed and an instrument rules flight plan was filed for the 14 Code of Federal Regulations Part 135 Air Taxi flight to Witham Field (SUA), Stuart, Florida. The airline transport pilot in command (PIC), co-pilot, cabin service representative, and two passengers reported no injuries. The flight originated from Republic Airport (FRG), Farmingdale, New York, at 1229. The PIC stated that while passing through 35,000 feet mean sea level, the flight crew heard a sound similar to a compressor stall, followed by a loss of power on the right engine. He immediately declared an emergency with air traffic control (ATC) and initiated the checklist items for engine shutdown in-flight. The cabin service representative came to the cockpit and informed him that the No. 4 outer window pane on the right side of the airplane had separated. The flight crew assumed the window pane had been ingested into the right engine. The PIC then contacted ATC and received clearance to return to FRG. The flight crew made a visual approach to FRG, landing at 1318, and taxied to the ramp without further incident. A bore scope examination of the engine was conducted and revealed the engine sustained a compressor stall and flamed out as a result of debris from the No. 4 outer window pane being ingested into the right engine. Foreign matter was attached to the high pressure stage 1 turbine blades. The combustion cans were clean. The high pressure compressor stage 1 blades were damaged. The high pressure nozzle guide vanes were not damaged. The engine was removed and a new engine was installed on the airplane. Review of the aircraft log books revealed that the No. 4 right window had been inspected every 72 months and at each emergency exit window release check, with no anomalies noted. The window was last inspected on June 9, 2009, and had accumulated 15,065 hours and 8,526 cycles since new. No anomalies were found during the inspection. The window was sent to the NTSB Materials Laboratory for further analysis. Examination of the window revealed the fractures in the outer pane of the window originated from an area of preexisting progressive cracking emanating from the exterior surface of the window. The cracking in the window did not initiate from local surface damage or scratches. There were no signs of any impact from aerodynamic forces and the window did not exhibit any indication of surface crazing (parallel small cracks perpendicular to the maximum tensile stress). The initial cause of the cracking could not be determined.