For N+2 ( N⩾4) body problem, if N bodies are at the vertices of a unit regular polygon base and the ( N+1)th body and the ( N+2)th body have equal masses and are at two ends of the vertical line of the plane P formed by the former N bodies, and the vertical line passes the geometrical center of the unit regular polygon and the geometrical center coincides with the center of masses m 1,…, m N , and m 1,…, m N , m N+1 , m N+2 (that is, the ( N+1)th body and the ( N+2)th body have the same distance from the center of masses), then the N+2 bodies form a double pyramidal central configuration if and only if the masses which are at the vertices of a regular polygon are equal and (1.6) holds.