We have made an experimental study of the tunnelling through a current-biased superconducting single electron transistor at temperatures down to 40 mK. The current-biased transistor consisted of two ultrasmall tunnel junctions connected in series, biased through two high-Ohmic resistors (length 10 μm) located very close to the tunnel junctions. The two-probe measurement of the current-voltage characteristic has shown a periodic modulation with a gate voltage, having two separate fundamental periods in gate charge, ΔQ1=e and ΔQ2=2e, as well as higher harmonics of these two. We have found that the amplitude of the 2e-component was enhanced as superconductivity of the electrodes was suppressed with an external magnetic field. These results are discussed within the context of a parity model.