A non-repulsive fixed point theorem is proved for upper semicontinuous, set-valued, acyclic and sequentially condensing transformations, $T$, of a convex, bounded, closed and infinite dimensional set, $C$, of a Banach space $E$ into itself. It is also shown that in certain cases a sequentially condensing map can be made condensing with the choice of a suitable new measure of non-compactness.