A putter comprises a handle at an upper end of a shaft of the putter to be grasped by one hand of a user, while an upper portion of the shaft between the handle and the head is to be grasped by a second hand of the user. The handle is arranged for swiveling movement relative to the upper shaft portion along a predetermined angular path defined about a transverse handle axis distinct from a shaft axis so that the handle can be fixedly held by the user and the shaft displaced in forward swinging movement along the predetermined angular path for hitting a golf ball. A putter head is pivotally connected at a lower end of the shaft to be movable about a distinct transverse pivot axis between a starting position in which a hitting plane is substantially parallel to the shaft axis and oblique ending position in which the hitting plane forms an acute angle therewith, such that the hitting plane of the head can remain substantially normal to the support surface after initial contact with the golf ball during the forward swinging movement.