A height adjustment device for a hinge having one hinge leaf that can be snapped into or inserted into a receiving part mounted on a door leaf or on a door frame, and with a height adjustment mechanism in the receiving part which has abutment against an edge of the hinge leaf. The height adjustment mechanism has a slide that is limitedly movable in the receiving part, and a rotatable height adjustment member. The slide has a portion for abutment against an edge of the hinge leaf. The height adjustment member has a plurality of radially directed, angularly separated arms of different lengths, wherein an end portion of such an arm is adapted to engage with an adapted engaging portion of the slide.