In most length-measuring interferometers, the measuring retroreflector must move along a straight line. Only small deviations from this straight line are permitted; otherwise the interference signal becomes too weak. The interferometer can be made immune to movements perpendicular to the straight line by adding a plane mirror to it. The problem of alignment of the extra mirror, which is very critical in existing schemes, is solved by reflecting the reference beam in this plane mirror. However, the perpendicular movements partly alter the course of the optical path. The resulting loss in accuracy when using standard optical elements can be kept below 0.5 µm. With error compensation, the loss in accuracy can be kept below 0.1 µm. For interferometric measurement applications that do not require the highest attainable precision, this is acceptable. If the lateral position of the return beam is restored just prior to each measurement, the accuracy of this optical scheme is comparable to that of a standard one.