A two way razor is disclosed having a handle, a bracket, and a shaving head mounting dual opposing shaving cartridges each comprising a plurality of razor blades, and a swivel mechanism disposed between the handle and the bracket for exchanging the positions of the first and second cartridges' positions, the swivel mechanism comprising first and second disks where a first disk has two projections at opposite ends and a second disk has two recesses at opposite ends, such that the projections and recesses engage to lock the bracket in first and second orientations with respect to the handle.