  Let $\mathscr{F}$ be a singular holomorphic foliation, of codimension $k$, on
a complex compact manifold such that its singular set has codimension $\geq
k+1$. In this work we determinate Baum-Bott residues for $\mathscr{F}$ with
respect to homogeneous symmetric polynomials of degree $k+1$. We drop the
Baum-Bott's generic hypothesis and we show that the residues can be expressed
in terms of the Grothendieck residue of an one-dimensional foliation on a
$(k+1)$-dimensional disc transversal to a $(k+1)$-codimensional component of
the singular set of $\mathscr{F}$. Also, we show that Cenkl's algorithm for
non-expected dimensional singularities holds dropping the Cenkl's regularity
assumption.
