The excitation function of the reaction (22)Ne(alpha,n)(25)Mg, the key neutron source in the astrophysical s process in massive stars, has been determined from threshold at E(alpha) = 570 up to 1450 keV with an experimental sensitivity of 10(-11) b. For all resonances in this energy range new resonance parameters have been measured. For a possible resonance at about 635 keV a new upper limit omega gamma < 60 neV for the strength was obtained. Based on the new data, improved reaction rates were calculated as a function of temperature. The new uncertainty limits are considerably smaller than in previous determinations, ruling out the large enhancement factors, up to 500, assumed in some stellar model calculations.