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Eigenfunctions and eigenvalues of the operator of the square of the angularmomentum are studied. It is shown that neither from the requirement for theeigenfunctions be normalizable nor from the commutation relations it ispossible to prove that the eigenvalues spectrum is a set of only integernumbers (in units $\hbar=1$). We present regular, normalizable eigenfunctionswith the non-integer eigenvalues thus demonstrating that a non-integer angularmomentum is admissible from the theoretical viewpoint.

Critical comments on quantization of the angular momentum: I. Analysis  based on the physical requirement on eigenfunctions and on the commutation  relations