We present a measurement of form-factor-independent angular observables in the decay B0→K∗(892)0μ+μ−. The analysis is based on a data sample corresponding to an integrated luminosity of 1.0 fb−1, collected by the LHCb experiment in pp collisions at a center-of-mass energy of 7 TeV. Four observables are measured in six bins of the dimuon invariant mass squared q2 in the range 0.1<q2<19.0 GeV2/c4. Agreement with recent theoretical predictions of the standard model is found for 23 of the 24 measurements. A local discrepancy, corresponding to 3.7 Gaussian standard deviations is observed in one q2 bin for one of the observables. Considering the 24 measurements as independent, the probability to observe such a discrepancy, or larger, in one is 0.5%.