The discovery of neutrino oscillations provides evidence that the Standard Model neutrinos have mass. Many models generate the mass for the light neutrinos by postulating the existence of heavy neutrinos. This thesis presents the search for a heavy Majorana neutrino decaying into a W boson and a muon that was performed using the ATLAS detector at the LHC. The search is performed using final states with two same-sign muons, two or more high momentum jets and low missing transverse energy. The events are required to pass the ATLAS muon trigger and the improvements made in the muon trigger algorithms are also presented. The data used in this thesis were collected using pp collisions at sqrt(s) = 7 TeV in 2011 and correspond to an integrated luminosity of 4.7 fb-1. In the search no excess of events above the background prediction is observed and 95% confidence level upper limits are set on the cross section times branching ratio for the production of heavy Majorana neutrinos. Limits are set for heavy Majorana neutrinos with masses ranging from 100 to 300 GeV, in which the observed limits range between 28 to 3.4 fb. These are most stringent direct limits to date for heavy neutrino masses larger than 100 GeV.