  We present a new method for constructing affine families of complex Hadamard
matrices in every even dimension. This method has an intersection with the
Di\c{t}\u{a} construction and it generalizes the Sz\"oll\H{o}si's method. We
reproduce well-known results, extend some families and present new families of
complex Hadamard matrices in even dimensions. In particular, found more than 13
millon inequivalent affine families of complex Hadamard matrices in dimension
32. We also find analytical restrictions for any set of four mutually unbiased
bases existing in dimension six.
