This work proposes a set-valued extension of the classical unknown input observers for linear continuous-time systems without using set-by-step set-membership computations or imposing the positivity property of the dynamics of the estimation error. In fact, based on an explicit set-integrationmethod of the estimation error, the framing and convergence properties of the proposed set-valued unknown input observer are demonstrated. Moreover, thanks to the proposed design approach, robust threshold on the residual can be established a priori. Simulation results are reported to highlight the effectiveness of the proposed state estimator in the presence of unknown inputs.