In general, we know that the higher direct images of finite morphisms are zero.

Now, suppose we have a morphism $f: S\rightarrow B$ which is finite over a Zariski open subset (say $Z$) of the projective variety $B$. But, the fibers over the points of the complement of $Z$ are not finite.

In the above situation can we still say $Rf_* = f_*$?