The invention relates to a ribbed power transmission belt having a tooth set made of elastomer based on ethylene/alpha-olefin elastomer, characterized in that at least the flanks of the teeth are coated with a film of thermoplastic which is at least partially cross-linked, containing at least 30% of at least one low-density polyethylene with a molecular mass ranging between 50 000 and 200 000 g/mole. The invention also relates to a manufacturing method which applies such a film of thermoplastic in the uncrosslinked or at least partially cross-linked state.