A self-complementary metasurface is studied in this paper. The metasurface is a 2-D periodical arrangement of unit cells formed by a metallic printed split ring resonator and its complementary counterpart. It is demonstrated that this structure behaves like a very selective band-pass filter for a certain linear polarization while band-stop filtering is achieved for the orthogonal polarization over the same frequency range. This idea opens the door to a new class of frequency selective surfaces made of connected and unconnected elements, whose filtering properties are mechanically tunable from band-pass to band-stop by rotating the surface or the polarization.