Provided that a cohomological model for G\documentclass[12pt]{minimal}
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\begin{document}$$G$$\end{document} is known, we describe a method for constructing a basis for n\documentclass[12pt]{minimal}
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\begin{document}$$n$$\end{document}-cocycles over G\documentclass[12pt]{minimal}
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\begin{document}$$G$$\end{document}, from which the whole set of n\documentclass[12pt]{minimal}
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\begin{document}$$n$$\end{document}-dimensional n\documentclass[12pt]{minimal}
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\begin{document}$$n$$\end{document}-cocyclic matrices over G\documentclass[12pt]{minimal}
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\begin{document}$$G$$\end{document} may be straightforwardly calculated. Focusing in the case n=2\documentclass[12pt]{minimal}
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\begin{document}$$n=2$$\end{document} (which is of special interest, e.g. for looking for cocyclic Hadamard matrices), this method provides a basis for 2-cocycles in such a way that representative 2\documentclass[12pt]{minimal}
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\begin{document}$$2$$\end{document}-cocycles are calculated all at once, so that there is no need to distinguish between inflation and transgression 2-cocycles (as it has traditionally been the case until now). When n>2\documentclass[12pt]{minimal}
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\begin{document}$$n>2$$\end{document}, this method provides an uniform way of looking for higher dimensional n-cocyclic Hadamard matrices for the first time. We illustrate the method with some examples, for n=2,3\documentclass[12pt]{minimal}
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\begin{document}$$n=2,3$$\end{document}. In particular, we give some examples of improper 3-dimensional 3\documentclass[12pt]{minimal}
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\begin{document}$$3$$\end{document}-cocyclic Hadamard matrices.
