  A new method of obtaining a sequence of isolated complex Hadamard matrices
(CHM) for dimensions $N\geqslant 7$, based on block-circulant structures, is
presented. We discuss, several analytic examples resulting from a modification
of the Sinkhorn algorithm. In particular, we present new isolated matrices of
orders $9$, $10$ and $11$, which elements are not roots of unity, and also
several new multiparametric families of order $10$. We note novel connections
between certain eight-dimensional matrices and provide new insights towards
classification of CHM for $N\geqslant 7$. These contributions can find real
applications in Quantum Information Theory and constructions of new families of
Mutually Unbiased Bases or Unitary Error Bases.
