A new search signature for excited leptons is explored. Excited muons are sought in the channel , assuming both the production and decay occur via a contact interaction. The analysis is based on 20.3 fb−1 of pp collision data at a centre-of-mass energy of taken with the ATLAS detector at the large hadron collider. No evidence of excited muons is found, and limits are set at the 95% confidence level on the cross section times branching ratio as a function of the excited-muon mass . For between 1.3 and 3.0 TeV, the upper limit on ) is between 0.6 and 1 fb. Limits on are converted to lower bounds on the compositeness scale Λ. In the limiting case , excited muons with a mass below 2.8 TeV are excluded. With the same model assumptions, these limits at larger masses improve upon previous limits from traditional searches based on the gauge-mediated decay .