A linear stepper motor is used for the displacement of an armature parallel to a stator having N steps. The stator includes (N+2) stator pole pieces which are enclosed by a magnetic guiding element and are each approximately the same distance from neighboring stator pole pieces. Furthermore, at least one coil is located between two stator pole pieces. The armature is enclosed by the stator in the radial direction and has a permanent magnet magnetized parallel to the stator which is disposed between two armature pole pieces. As a result of the reluctance forces, the armature occupies stable idle positions inside the stator in which the stator pole pieces lie opposite the armature pole pieces. By energizing the coils with a short current pulse, the armature can be displaced inside the stator between the different stable idle positions.