In previous studies, we showed that the branch length similarity (BLS) entropy profile could be used successfully for the recognition of shapes such as battle tanks, facial expressions, and butterflies. In the present study, we introduce critical points defined as a set of distinguishing points with high curvature to the BLS entropy profile in order to improve the shape recognition. In order to generate a given number of critical points from the shape, we propose a critical point detection method. Furthermore, we show the invariant properties of the BLS entropy deor. To evaluate the effects of critical points on the shape recognition of the BLS entropy deor, we performed a butterfly classification experiment against a real image data set, and we conducted performance comparisons with other point detection methods. In addition, the performance of the BLS entropy deor computed using the critical points was compared with those of other well-known deors such as the Fourier deor using three machine learning techniques, the Bayesian classifier, the multi-layer perceptron and the support vector machine. The results show that the BLS entropy deor outperforms other well-known deors.