  In this paper we study unitary solutions of the associative Yang--Baxter
equation (AYBE) with spectral parameters. We show that to each point $\tau$
from the upper half-plane and an invertible $n \times n$ matrix $B$ with
complex coefficients one can attach a solution of AYBE with values in $Mat_{n
\times n}(\CC) \otimes Mat_{n \times n}(\CC)$, depending holomorphically on
$\tau$ and $B$. Moreover, we compute some of these solutions explicitly.
