In general cases of pattern recognition, a pattern to be recognized is first represented by a set of features and the measured values of the features are then classified. Finding features relevant to recognition is thus an important issue in recognizer design. As a fundamental design framework taht systematically enables one to realize such useful features, the Subspace Method (SM) has been extensively used in various recognition tasks. However, this promising methodological framework is still inadequate. The discriminative power of early versions was not very high. The training behavior of a recent discriminative version called the Learning Subspace Method has not been fully clarified due to its empirical definition, though its discriminative power has been improved. To alleviate this insufficiency, we propose in this paper a new discriminative SM algorithm based on the Minimum Classification Error/Generalized Probabilistic Descent method and show that the proposed algorithm achieves an optimal accurate recognition result, i.e., the (at least locally) minimum recognition error situation, in the probabilistic descent sense.