This paper presents a new tau-lepton reconstruction and identification procedure at the ATLAS detector at the Large Hadron Collider, which leads to significantly improved performance in the case of physics processes where a highly boosted pair of tau-leptons is produced and one tau-lepton decays into a muon and two neutrinos (tau mu), and the other decays into hadrons and one neutrino (tau had). By removing the muon information from the signals used for reconstruction and identification of the tau had candidate in the boosted pair, the efficiency is raised to the level expected for an isolated tau(had). The new procedure is validated by selecting a sample of highly boosted Z ->tau(mu) tau(had) candidates from the data sample of 140 fb(-1) of proton-proton collisions at 13 TeV recorded with the ATLAS detector. Good agreement is found between data and simulation predictions in both the Z ->tau(mu) tau(had) signal region and in a background validation region. The results presented in this paper demonstrate the effectiveness of the tau(had) reconstruction with muon removal in enhancing the signal sensitivity of the boosted tau(mu)tau(had) channel at the ATLAS detector.