Control allocation is related to control of overactuated systems, and provides a method of distributing the total control demand among the individual actuators. Using linearization, control allocation of virtual input v is equivalent to linear inverse problem with interval-constrained vector u, which we need to figure out: v=Bu, where B has more columns than rows. The problem can be solved by linear or quadratic programming, but this solution in some cases cannot be adopted due to the safety sertification issues or high complexity of optimization routines for on-board realization. We propose a method for calculating u, which is based on control box bisection and explicit description of its image in the form of a system of linear inequalities.