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We give a construction for regular Hadamard matrices of order $a^{2}v$ where $a\ne 1$ is the order of a Hadamard matrix and $v$ is the order of a regular Hadamard matrix. The construction can be used to construct regular Hadamard matrices with special properties and includes several constructions which have been given previously. In the final section we consider the case $a=2$ in more detail.