A barber or straight edge razor houses a replaceable blade and includes a body member having a handle and a blade-receiving base portion, a clamp member detachably hinged to the base portion to comprise opposite halves of the razor, and bias apparatus between the razor halves above the hinge for urging the lower portions of the razor halves relatively toward each other to retain the blade therebetween. The blade is releasable by moving the upper portions of the razor halves relatively toward one another. Along a rear gripping portion of the razor halves, one of the halves is structured to assume substantially all of the normal gripping forces so as to prevent inadvertent release of the blade, while the halves include a forward region which is structured to receive special pinching forces to release the blade. Upwardly and rearwardly inclined ridges in the blade-retaining region may be provided to aid in upward seating of the blade as it is moved rearwardly into the razor. Also, the hinge pivot pins may be integral with one of the razor halves and hinge tubes are integral with the other.