Alternative set of defining constants for redefinition of four SI units

We discuss different sets of defining constants, fixed values of which are considered in connection with the transition to new definitions of four SI units (the kilogram, the mole, the ampere, and the kelvin). The notion of constant's order in a given system of units is suggested. We propose an alternative set of fixed constants applicable for new definitions of the four SI units. We analyse and discuss in detail the set, which consists of the Planck constant, the Avogadro constant, the Boltzmann constant and the magnetic constant.