We propose a type of lossless nonlinear polarizer, novel to our knowledge, a device that transforms any input state of polarization (SOP) of a signal beam into one and the same well-defined SOP toward the output, and perform this without any polarization-dependent losses. At the polarizer output end, the signal SOP appears to be locked to the input pump SOP. The polarizer is based on the nonlinear Kerr interaction of copropagating signal and pump beams in a telecom or randomly birefringent optical fiber.