  We shall give an example of irreducible symplectic manifolds X and Y which
are not bimeromorphic, but have the same periods in the second cohomologies.
More explicitly, X and Y are generalized Kummer varieties of dim 4 for a
general complex torus T of dim 2 and its dual torus T^*. A key result is an
observation of Shioda for the periods of T and T^*. As a concluding remark, we
shall discuss the difference between our case and Kummer surfaces.
