Consider an electrical dipole and a magnetic loop—co-centered and axially aligned. This compact pair of line antennas is centro-symmetric and polarization-sensitive but suffers no mutual coupling. Their “spatial matched filter” beam-steering bias will be analytically derived here for the first time in the open literature. The key findings include the following: 1) The elevation-azimuthal directional beam-pattern is multiplicatively separable from the polarizational beam-pattern. 2) No pointing bias exists in polarization (i.e., the nominal “look polarization” always gives the actual peak polarization). 3) No polarizational sidelobe exists. 4) The actual peak polar direction is always normal to the “co-centered orthogonal loop and dipole” array axis regardless of the nominal polar “look direction.”