This paper gives constructive methods for embedding a dicyclic solution of a balanced incomplete block design with parameters \((2t+1,4t+2,2t,t,t- 1)\) in a Hadamard matrix of order \(4t+4\). In a recent paper [Three new dicyclic solutions of (21,42,20,10,9)-designs, J. Comb. Theory, Ser. A 40, 427-428 (1985; Zbl 0575.05009)] the first and third authors present three dicyclic solutions of (21,42,20,10,9)-designs. The current authors then use these designs to construct the three new Hadamard matrices of order 44 promised by the construction described earlier in the paper.