The Mean Pulse Profile of PSR J0737-3039A

General relativity predicts that the spin axes of the pulsars in the double-pulsar system (PSR J0737-3039A/B) will precess rapidly, in general leading to a change in the observed pulse profiles. We have observed this system over a one-year interval using the Parkes 64-m radio telescope at three frequencies: 680, 1390 and 3030 MHz. These data, combined with the short survey observation made two years earlier, show no evidence for significant changes in the pulse profile of PSR J0737-3039A, the 22-ms pulsar. The limit on variations of the profile 10% width is about 0.5 deg per year. These results imply an angle delta between the pulsar spin axis and the orbit normal of <~ 60 deg, consistent with recent evolutionary studies of the system. Although a wide range of system parameters remain consistent with the data, the model proposed by Jenet & Ransom (2004) can be ruled out. A non-zero ellipticity for the radiation beam gives slightly but not significantly improved fits to the data, so that a circular beam describes the data equally well within the uncertainties.