Hadamard partitioned difference families and their descendants

If D is a (4u2,2u2-u,u2-u) Hadamard difference set (HDS) in G, then {G,G\D} is clearly a (4u2,[2u2-u,2u2+u],2u2) partitioned difference family (PDF). Any (v,K,)-PDF will be said a Hadamard PDF if v=2 as the one above. We present a doubling construction which, starting from any Hadamard PDF, leads to an infinite class of PDFs. As a special consequence, we get a PDF in a group of order 4u2(2n+1) and three block-sizes 4u2-2u, 4u2 and 4u2+2u, whenever we have a (4u2,2u2-u,u2-u)-HDS and the maximal prime power divisors of 2n+1 are all greater than 4u2+2u.