A novel technique for deriving lower bounds on the error probability when communicating one of M signals over a communication channel is proposed. At the basis of the technique, stands an improvement on a recent lower bound on the probability of a union of events by de Caen. The new bound includes a function which can be optimized in order to achieve the tightest results. By applying this bound to the problem of lower bounding the error probability, while suggesting an appropriate optimization function, in the spirit of the relevant channel model and type of the code, new bounds on the error probability can be derived. In this talk, we apply the new bound to the problem of lower bounding the error probability of binary linear codes over the Binary Symmetric Channel (BSC). The resulting bound improves on the latest bound appearing in the current literature, by Keren and Litsyn.