Abstract The e+e−→μ+μ− reaction has been studied at centre of mass energies ranging between 38.3 abd 46.8 GeV with the CELLO detector at PETRA. We present results on the cross section and the charge asymmetry for this channel. Combining all the data at the average energy 〈 s 〉=43 GeV we obtain Rμμ=〈σμμ/σ0〉=0.98±0.04±0.04, 〈Aμμ〉=(−14.1±3.7±1.0)%, where σ0 is the QED cross section and Aμμ is the charge asymmetry corrected for pure radiative effects. These results are in good agreement with the expected values of Rμμ=1.01 and Aμμ=−14.5% at that energy.