We propose a new method to optimize the completely-trained boosted cascade detector on an enforced training set. Recently, due to the accuracy and real-time characteristics of boosted cascade detectors like the Adaboost, a lot of variant algorithms have been proposed to enhance the performance given a fixed number of training data. And, most of algorithms assume that a given training set well exhibits the real world distributions of the target and non-target instances. However, this is seldom true in real situations, and thus often causes higher false-classification ratio. In this paper, to solve the optimization problem of completely trained boosted cascade detector on false-classified instances, we propose a new base hypothesis weight optimization algorithm called DOOMRED (Direct Optimization Of Margin for Rare Event Detection) using a mathematically derived error upper bound of boosting algorithms. We apply the proposed algorithm to a cascade structured frontal face detector trained by AdaBoost algorithm. Experimental results demonstrate that the proposed algorithm has competitive ability to maintain accuracy and real-time characteristic of the boosted cascade detector compared to those of other heuristic approaches while requiring reasonably small amount of optimization time.