The elevator of the invention comprises a set of hoisting ropes, an elevator car suspended by the set of hoisting ropes and possibly a counterweight suspended by the set of hoisting ropes. The hoisting ropes are received by pair of rope pulleys, and they have been arranged to run from a first rope pulley of the pair of rope pulleys to a second rope pulley of the pair of rope pulleys. The rope pulleys are rotatably mounted with bearings on the mounting frame (23), which comprises at least one first connecting part (24), by means of which the rope pulley is secured to a mounting support on the elevator car or counterweight. The mounting frame of each rope pulley in the pair of rope pulleys is provided with at least one second connecting part (25), which has been arranged to be connected with accurate alignment to an aligning means (20,21) separate from the mounting support.