A shape memory actuator includes a supporting body, a driven element pivotably mounted on the supporting body and in permanent contact with a driving element whose movement is determined by a SMA actuating member and by at least one resilient return member acting in opposition to the SMA actuating member. The driven element is able to take two stable positions under the action of a bistable moving system connecting the driving element to the driven element such that each toggling between the two stable positions is due to an activation of the SMA actuating member, the latter being arranged together with the bistable moving system. The resilient return member, the driving element and the driven element on a same side of the supporting body are in a substantially co-planar arrangement.