This paper presents a search for exotic decays of the Higgs boson into a pair of new pseudoscalar particles, H→aa, where one pseudoscalar decays into a b-quark pair and the other decays into a τ-lepton pair, in the mass range 12≤ma≤60  GeV. The analysis uses pp collision data at s=13  TeV collected with the ATLAS detector at the LHC, corresponding to an integrated luminosity of 140  fb-1. No significant excess above the Standard Model (SM) prediction is observed. Assuming the SM Higgs boson production cross section, the search sets upper limits at 95% confidence level on the branching ratio of Higgs bosons decaying into bb¯τ+τ-, B(H→aa→bb¯τ+τ-), between 2.2% and 3.9% depending on the pseudoscalar mass.