Using the method of two-component MHD and also the results (Nikolov and Nedeltcheva 1972, Nikolov et al. 1981) for the averaged Miller's forces, the theory of a plane resonance probe is extended for the case of a constant magnetic field parallel to the probe surface. Theoretically three resonance frequencies are obtained, two of them coinciding with well known results at B0=0. The third resonance can only be found when an external magnetic field is applied. When the Langmuir frequency greatly exceeds the Larmor frequency, this resonance tends to the ion Larmor frequency, while in the opposite case it tends to the ion Langmuir frequency.