  We suggest a method to experimentally obtain two-dimensional matter-wave
discrete solitons with a {\it self-repulsive} BEC in optical lattices. At the
edge of the Brillouin zone, a wave packet effective mass is negative which
could be treated as inversion of the nonlinearity sign. Above critical
nonlinearity this makes the wave packets collapse partially into localized
modes with a chemical potential located in the gap between the first and the
second bands. This critical nonlinearity is also associated with the smallest
nonlinearity for which the discrete solitons are possible in the gap. Extensive
numerical simulations for square and asymmetric honeycomb lattices in
continuous model illustrate every stage of the process.
