Abstract: Fittings for connecting H-shaped beams and columns of a steel frame construction, each fitting comprising an L-shaped outer fitting member connecting an outer surface of a flange of the beam to the column by means of bolts and an L-shaped inner fitting member connecting an inner surface of the flange of the beam to the column by means of bolts having a space for receiving therein a web of the beam, thereby embracing the flange of the beam between the L-shaped outer and inner fitting members to provide two surface frictional engagements. A column side plate of each the L-shaped fitting members successively increases its thickness from a free end to a portion connected to the beam side plate thereof.