We present a precise measurement of the neutron magnetic form factor G(mm) at low momentum transfer (q = 1.69 fm-1). From a simultaneous measurement of D(e, e'n) and D(e, e'p) we obtain the ratio of neutron and proton cross sections. The neutron detection efficiency is obtained from a separate measurement using tagged neutrons produced by H(n,p)n scattering of a monochromatic neutron beam. In contrast to previous determinations of G(mm), the present value is insensitive to the systematic uncertainties in the interpretation of the data in terms of G(mm) and represents a determination of G(mm) to +/- 1.7%.