  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.
