An exchange functional is proposed which is conceptually similar to the established Becke functional and satisfies the same asymptotic properties. The one-parameter variant A of this new functional yields atomic exchange energies which are very close to those from the optimized potential model (OPM) for the light elements (up to Ne), whereas the three-parameter variant B reproduces the OPM reference values for all elements (H to Xe) more accurately than other established exchange functionals. For molecular applications, the new exchange functional is combined with a new non-local correlation functional based on a Coulomb hole model. Detailed results are reported for the molecules from the G2 data base. For each of the four basis sets considered, variants A and B yield essentially the same atomization energies, ionization potentials, proton affinities and molecular geometries. The mean absolute deviation between the calculated and experimental atomization energies for the G2 reference molecules is 3 kcalmol-1. In an overall assessment, the present results seem comparable in quality with those from the B3LYP hybrid functional, even though our new functional does not include any Hartree–Fock exchange. Some illustrative results for transition-metal compounds are also given.