A search is performed for heavy Majorana neutrinos (N) using an event signature defined by two muons of the same charge and two jets ((\mu^{±}\mu^{±}jj)). The data correspond to an integrated luminosity of 19.7 fb⁻¹ of proton-proton collisions at a center-of-mass energy of 8 TeV, collected with the CMS detector at the CERN LHC. No excess of events is observed beyond the expected standard model background and upper limits are set on (|V_{\mu N}|^{2}) as a function of Majorana neutrino mass mN for masses in the range of 40-500 GeV, where (V_{\mu N}) is the mixing element of the heavy neutrino with the standard model muon neutrino. The limits obtained are (|V_{\mu N}|^{2}) < 0.00470 for (m_{N}) = 90 GeV, (|V_{\mu N}|^{2}) < 0.0123 for (m_{N}) = 200 GeV, and (|V_{\mu N}|^{2}) < 0.583 for (m_{N}) = 500 GeV. These results extend considerably the regions excluded by previous direct searches.