Magnetic properties of a $sigma-$Fe$_{16}$Cr$_{14}$ alloy calculated with the charge and spin self- consistent Korringa-Kohn-Rostoker (KKR) and combined with coherent potential approximation (KKR-CPA) methods are reported. Non-magnetic state as well as various magnetic orderings were considered, i.e. ferromagnetic (FM) and more complex anti-parallel (called APM) arrangements for selected sublattices, as follows from the symmetry analysis. It has been shown that the Stoner criterion applied to non-magnetic density of states at the Fermi energy, $E_F$ is satisfied for Fe atoms situated on all five lattice sites, while it is not fulfilled for all Cr atoms. In FM and APM states, the values of magnetic moments on Fe atoms occupying various sites are dispersed between 0 and 2.5 $mu_B$, and they are proportional to the number of Fe atoms in the nearest-neighbor shell. Magnetic moments of Cr atoms havin much smaller values were found to be coupled antiparallel to those of Fe atoms. The average value of the magnetic moment per atom was found to be $<mu>=0.55 mu_B$ that is by a factor of 4 larger than the experimental value found for a $sigma-$Fe$_{0.538}$Cr$_{0.462}$ sample. Conversely, admitting an anti- parallel ordering (APM model) on atoms situated on C and D sites, according to the group theory and symmetry analysis results, yielded a substantial reduction of $<mu>$ to 0.20 $mu_B$. Further diminution of $<mu>$ to 0.15 $mu_B$, which is very close to the experimental value of 0.14 $mu_B$, has been achieved with the KKR-CPA calculations by considering a chemical disorder on sites B, C and D.
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