This paper is a continuation of the paper by S. Grigelionis [2]. The study of the first neighbourhood of non-holonomic hypercomplex element of the projective space $P_4$ is continued (in the previous paper [2] a non-holonomic hypercomplex was called a non-holonomic complex), but the attention is paid mainly to problems of intrinsic normalizations of such non-holonomic hypercomplexes. So called intrinsic normal spaces of the first and the second kind, an intrinsic normal plane, an intrinsic normal line and some one-to-one correspondences between the normal spaces are obtained. The geometrical interpretations of all these objects and correspondences are given.