The object of the invention is a tensioning arrangement for a traction means of an elevator, which arrangement comprises at least an elevator car configured to move up and down in an elevator hoistway and at least one or more compensating weights, which are for their part connected to support the elevator car by the aid of their own support means, such as by the aid of ropes or belts and also of diverting pulleys, and a hoisting machine provided with at least one traction sheave or corresponding, and also at least one traction means (7) such as a belt, rope or chain, which is configured to transmit the rotational movement of the traction sheave into movement of the elevator car and of the compensating weights. The traction means (7) is fixed from at least one of its ends to a fixing means (1) providing an essentially constant tensioning force.