In section 1 the results of the author's previous paper [4] are given, where the structure $f(2k+l,-l)$ was defined on the manifold $M^n$. In section 2, 3 and 4 there are new results which refer to structure $-f^k=\phi$ of a rank $f=n-l$. The hypersurface $N^{n-1}$ of the manifold $M^n$ is observed and it Is shown that $\phi$ induces on $N^{n-1}$ a natural structure $F=B^{-1}\phi B$, which is a $F(3,-1)$-structure, or an almost product structure, which depends on the choice of the hypersurface. Examined also are the integrability conditions of the naturally induced $F(3,-1)$-structure.