We present the results of an experimental study of the nucleation of superconductivity at the surface of a single crystal YB$_6$ in a tilted dc magnetic field. A recently developed experimental technique allowed us to determine $H_{c3}$ at each side of the sample as a function of the angle between the dc magnetic field and the surface. Experiment shows that the ratio $H_{c3}/ H_{c2}approx 1.28 $ in the direction perpendicular to the surface dc field while according to the theory this ratio should be equal to 1. This sharp distinction cannot be ascribed to the surface roughness.
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