  We study the existence of Gabor orthonormal bases with window the
characteristic function of the set W=[0,a] U [b+a, b+1] of measure 1, with a,
b>0. By the symmetries of the problem, we can restrict our attention to the
case a<=1/2. We prove that either if a<1/2 or (a=1/2 and b>= 1/2) there exist
such Gabor orthonormal bases, with window the characteristic function of the
set W, if and only if W tiles the line. Furthermore, in both cases, we
completely describe the structure of the set of time-frequency shifts
associated to these bases
