To reduce the required number of bolts for joining steel frames to each other.

In this connection structure for bolting the steel frames 1 and 2 used as the columns and beams of a building through auxiliary plates 5 and 6 so as to joint the steel frames to each other, protruded rings 9 and grooves 10 engaged with the close-fitted surfaces of both of the steel frames 1 and the auxiliary plates 5 and 6 are formed by rolling and, with the protruded rings engaged with the grooves, the auxiliary plates are fitted closely to the steel frames and bolted to each other. The protruded rings and grooves are formed only on and in one frame 1 and the surfaces of the auxiliary plates 5 and 6 fitted closely thereto, and the steel frame and auxiliary plates are tightened to each other with ordinary bolts. A plurality of protruded rings and grooves are formed concentrically to each other around bolt holes 8, linearly along the lateral direction of the steel frames, or in a wedge shape facing the longitudinal direction of the steel frames.