One shows that the methods of M. Hakim, N. Sibony, and E. Løw, used by them for the construction of inner functions in a sphere, can be applied also in a more general situation. The fundamental result of the paper is: For any positive continuous function H on the unit sphere S of the space ℝ^d, there exists a real function u, harmonic in the unit ball[Figure not available: see fulltext.], such that the function ∇u is bounded in B and |∇u| =H almost everywhere on S.