  Let (V,0) be a germ of a complete intersection variety in \CC^{n+k}, n>0,
having an isolated singularity at 0 and X be the germ of a holomorphic vector
field on \CC^{n+k} tangent to V and having on V an isolated zero at 0. We show
that in this case the homological index and the GSV-index coincide. In the case
when the zero of X is also isolated in the ambient space \CC^{n+k} we give a
formula for the homological index in terms of local linear algebra.
