This paper presents a new approach for the contingency-constrained single-bus unit commitment problem. The proposed model explicitly incorporates an n-K security criterion by which power balance is guaranteed under any contingency state comprising the simultaneous loss of up to K generation units. Instead of considering all possible contingency states, which would render the problem intractable, a novel method based on robust optimization is proposed. Using the notion of umbrella contingency, the robust counterpart of the original problem is formulated. The resulting model is a particular instance of bilevel programming which is solved by its transformation to an equivalent single-level mixed-integer programming problem. Unlike previously reported contingency-dependent approaches, the robust model does not depend on the size of the set of credible contingencies, thus providing a computationally efficient framework. Simulation results back up these conclusions.