NEW : Crews recover the pilot 's body from the Hudson River , the FAA says . NEW : The next step is to remove the rest of the plane from the water , the New York State Police says . The vintage military jet crashed the day before near New York , Ulster .
NEW : Crews recover the pilot 's body from the Hudson River , the FAA says . NEW : The next step is to remove the rest of the plane from the water , the FAA says . The vintage military jet crashed Saturday near Ulster , New York .