  A symmetry extending the $T^2$-symmetry of the noncommutative torus $T^2_q$
is studied in the category of quantum groups. This extended symmetry is given
by the quantum double-torus defined as a compact matrix quantum group
consisting of the disjoint union of $T^2$ and $T^2_{q^2}$. The bicross-product
structure of the polynomial Hopf algebra of the quantum double-torus is
computed. The Haar measure and the complete list of unitary irreducible
representations of the quantum double-torus are determined explicitly.
