A model--independent search for deviations from the Standard Model prediction is performed using the full $e^\pm p$ data sample collected by the H1 experiment at HERA. All event topologies involving isolated electrons, photons, muons, neutrinos and jets with transverse momenta above 20 GeV are investigated in a single analysis. Events are assigned to exclusive classes according to their final state. A dedicated algorithm is used to search for deviations from the Standard Model in the distributions of the scalar sum of transverse momenta or the invariant mass of final state particles and to quantify their significance. Variables related to angular distributions and energy sharing between final state particles are also introduced to study the final state topologies. No significant deviation from the Standard Model expectation is observed in the phase space covered by this analysis.