Crucial to the successful development of a theoretical model for high-temperature superconductivity is knowledge of the symmetry of the order parameter (or wavefunction) that describes the pairing of electrons in the superconducting state. Several experimental studies(1-8) provide convincing evidence for an anisotropic order parameter, consistent with a d(x2-y2) symmetry, But none of these earlier experiments could rule out unambiguously an additional contribution from isotropic s-wave pairing; these experiments either involved superconductors with an orthorhombic crystal structure (for which a mixed s+d state is becoming increasingly recognized as a likely consequence(9,10)), or their interpretation required detailed modelling of the uncertain effects of disorder and defects. Here we report the results of an experiment designed to circumvent these difficulties : the material studied is the single-layer tetragonal superconductor Tl2Ba2CuO6+delta, and the experimental configuration is such that the interpretation of the results relies solely on symmetry considerations, Our results indicate that this material has pure d(x2-y2) pairing symmetry, so providing a starting point for understanding the more complex mixed s+d state that appears to characterize other high-temperature superconductors.