  The structure groups of non-degenerate symmetric set-theoretical solutions of
the quantum Yang-Baxter equation provide an infinite family of Garside groups
with many interesting properties. Given a non-degenerate symmetric solution, we
construct for its structure group a group of automorphisms. Moreover, we show
this group of automorphisms admits a subgroup that preserves the Garside
properties of the structure group. In some cases, we could also prove the group
of automorphisms obtained is an outer automorphism group.
