We search for lepton-flavor and lepton-number-violating τ decays into a lepton (ℓ= electron or muon) and two charged mesons (h,h′=π± or K±) using 854 fb−1 of data collected with the Belle detector at the KEKB asymmetric-energy e+e− collider. We obtain 90% confidence level upper limits on the τ→ℓhh′ branching fractions in the range (2.0–8.4)×10−8. These results improve upon our previously published upper limits by factors of about 1.8 on average.