On (2n,2,2n,n) relative difference sets

In this article, we show that a (2n,2,2n,n) relative difference set in a group G of order 4n exists only if a Sylow 2-subgroup of G is non-cyclic and n is even unless n=1. We also construct (2n,2,2n,n) relative difference sets relative to non-normal subgroups.