[en] For calculations of criticality perturbations it is necessary to use group constants which take into account not only the peculiarities of the intra-group flux but also those of the behaviour of the adjoint flux. A new method is proposed for obtaining bilinear-averaged constants of this type on the basis of the resonance characteristics of the importance function and the difference between the value of neutron importance at the group boundary and the group-averaged value (the bsup(+j) factor). A number of calculations are made for the ratios of reactivity coefficients in the BFS assemblies. Values have been obtained for the difference between the results of calculation with bilinear-averaged constants and those averaged conventionally (over flux). In many cases, this difference exceeds the experimental error. (author)