  A new type of complex Hadamard matrices of order 9 are constructed. The
studied matrices are symmetric, block circulant with circulant blocks ($BCCB$)
and form an until now unknown non-reducible and non-affine two-parameter orbit.
Several suborbits are identified, including a one-parameter intersection with
the Fourier orbit $F_{9}^{(4)}$. The defect of this new type of Hadamard
matrices is observed to vary, from a generic value 2 to the anomalous values 4
and 10 for some sub-orbits, and to 12 and 16 for some single matrices. The
latter matrices are shown to be related to complete sets of MUBs in dimension
9.
