Using harmonic superspace techniques we construct a new field realization of the Virasoro algebra. The main conformal objects are U(1) Cartan tensors instead of the U(1) Lorentz ones. The new conformal model, which admits moreover a {ital d}=2 (4,0) global supersymmetry, is constructed out of the infinitely relaxed Howe-Stelle-Townsend and Fayet-Sohnius hypermultiplets. The conformal current {ital T}{sup 4+} together with the harmonic superspace operator product expansion rules are given. The Virasoro algebra and the harmonic superspace Schwarzian derivative {ital S}{sup 4+} are also derived.