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The study completes a series of works devoted to spread of particles population in supercritical catalytic branching random walk (CBRW) on a multidimensional lattice. The rate of this spread depends essentially on the distribution tails of the random walk jump. So far, in case of regularly varying tails, we considered the problem of the scaled front propagation assuming independence of components of the random walk jump. Now, without this hypothesis, we examine an "isotropic" case, when the rate of decay of the jumps distribution in different directions is given by the same regularly varying function. We specify the probability that, for time going to infinity, the limiting random set formed by appropriately scaled positions of population particles belongs to a set B, containing the origin with its neighborhood, in R^d. In contrast to the previous analysis the random cloud of particles with normalized positions in the time-limit will not concentrate on coordinate axes with probability one.