We present a new measurement of the spin-dependent structure function g1 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 1 GeV2 < Q2 < 60 GeV2. This structure function is found to be negative at small x. The first moment Γ1 d=∫0 1g 1 ddx evaluated at Q0 2 = 10 GeV2 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 Γ1 p, we obtain Γ1 p - Γ1 n = 0.199 ± 0.038 which agrees with the Bjorken sum rule.