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We recursively construct a new family of ( 2^{6d+4}, 8, 2^{6d+4}, 2^{6d+1}) semi-regular relative difference sets in abelian groups G relative to an elementary abelian subgroup U. The initial case d=0 of the recursion comprises examples of ( 16,8,16,2) relative difference sets for four distinct pairs ( G,U).