A new reduction on the size of the search space for cocyclic Hadamard matrices over dihedral groups
is described, in terms of the so called
. This new search space adopt the form of a forest consisting of two rooted trees (the vertices representing subsets of coboundaries) which contains all cocyclic Hadamard matrices satisfying the constraining condition. Experimental calculations indicate that the ratio between the number of constrained cocyclic Hadamard matrices and the size of the constrained search space is greater than the usual ratio.