Abstract: Several embodiments of a golf club putter having a novel putter head with a striking face defined by two unequal radii are disclosed. In one embodiment, the convex striking face is defined by an upper radius and a lower radius meeting along a linear path to provide an single point of contact for the engagement of a golf ball. In a second embodiment, the upper radius and lower radius meet along an arcuate path, and a protruding bottom surface mimics this arcuate path, to provide an optimum point of contact for a golf ball regardless of the longitudinal angle of address of the putter. Dual radius putters having weighting schemes and composite or plastic inserts are also disclosed to further improve the true roll of a golf ball generated by an engagement with the instant putter.