  A new class of indecomposable, irretractable, involutive, non-degenerate
set-theoretic solutions of the Yang--Baxter equation is constructed. This class
complements the class of such solutions constructed in \cite{CO22} and together
they generalize the class of solutions described in \cite[Theorem 4.7{CO21}.
Necessary and sufficient conditions are found in order that these new solutions
are simple. For a rich subclass of these solutions the structure of their
permutation groups, considered as left braces, is determined. In particular,
these results answer a question stated in \cite{CO21}. In the finite case, all
these solutions have square cardinality. A new class of finite simple solutions
of non-square cardinality such that their permutation groups are simple left
braces is also constructed.
