We show that such modes can be reflected from the optical fiber facet. Due to reflection, a locking effect occurs near the optical fiber facet for the whispering gallery modes with an axial component of the wave vector. Effective locking occurs due to the destructive interference of the waves coming from the excitation source and the waves reflected from the fiber facet. We obtained an analytical expression for determining the resonant wavelengths. We also experimentally characterized the reflectance of the fiber edge by studying dynamics of an optical pulse propagating towards the edge and reflecting from it.