  We give sufficient conditions for the exponential system to be a Riesz basis
in $L^2(E)$, where $E$ is a union of two intervals. We show that these
conditions are close to be necessary. In addition, we demonstrate ``extra point
effect'' for such systems, i.e. it may happen that the Riesz basis in $L^2(E)$
differs by one point from the Riesz basis on an interval.
