Context. Optical interferometers are subject to many atmospheric and instrumental artifacts that contribute to the degradation of their instrumental contrast, hence their performances. The differential birefringence is, among these effects, one of the trickiest to control, in particular for instrument using fibers, where it can be far larger than the one arising in the optical mirror trains. Several solutions have been tested in the past, ranging from polarization splitting to fiber tweaking. We adopt a new solution for the PIONIER instrument, a four-telescope (4T) combiner at the Very Large Telescope Interferometer (VLTI). Aims. We present a method to cancel the instrumental birefringence in an optical interferometer, allowing the joint detection of the fringe patterns of both polarizations, and substantial gains to be made in both signal-to-noise ratio and readout speed. Methods. A thin (2 mm) plate of birefringent material (LiNbO 3 ) is inserted in each of the four beams. The incidence angle of each plate is adjustable. This allows us to introduce a controlled amount of birefringence in each beam and to cancel the instrumental differential birefringence. We present our derivation of the induced birefringence versus incidence angle and discuss the design choices. Results. Our proposed solution is implemented in the Pionier instrument. Before correction, the instrumental birefringence was of order 5 μm (path length). The adjustment takes about one hour, results in a birefringence of less than 0.1 μm, and is stable for at least the duration of an observing run (several days). Conclusions. We demonstrate on an operational near-infrared interferometer a novel, simple, low-cost, and effective technique to control the differential birefringence. The predictability and stability of the correction make this technique ideal for an automated correction in the VLTI second generation instruments.