We present a new measurement of the spin-dependent structure function g(1)(d) of the deuteron in deep inelastic scattering of 190 GeV polarised muons on polarised deuterons, in the kinematic range 0.003<x<0.7 and IGeV2,Q(2)<60GeV(2). This structure function is found to be negative at small x. The first moment Gamma(1)(d)=integral(0)(1)g(1)(d)dx evaluated at Q(0)(2)=10GeV(2) is 0.034+/-0.009(stat.)+/-0.006(syst). This value is below the Ellis-Jaffe sum rule prediction by three standard deviations. Using our earlier determination of Gamma(1)(p), we obtain Gamma(1)(p)-Gamma(1)(n)=0.199+/-0.038 which agrees with the Bjorken sum rule.