Title A generalization of a construction due to Van Nypelseer Author D. Leemans Reference Beitrage Algebra Geom. 46 (2005), nr. 2, 561-574. Abstract We give a construction leading to new geometries from Steiner systems or arbitrary rank two geometries. Starting with an arbitrary rank two residually connected geometry G, we obtain firm, residually connected, (IP)_2 and flag-transitive geometries only if G is a thick linear space or a (4,3,4)-gon. This construction is also used to produce a new firm and residually connected rank six geometry on which the Mathieu group M_24 acts flag-transitively.