Recognition of coding sequences in a complete genome is animportant problem in DNA sequence analysis. Their rapid and accurate recognition contributes to various relevant research and application. In this paper, we aim to distinguish the coding sequences from the non-coding sequences in a prokaryote complete genome. We select a data set of 51 available bacterial genomes. Then, we use the global descriptor method on the coding/non-coding primary sequences and obtain 36 parameters for each coding/non-coding primary sequence. These parameters are used to generate some spaces, whose points represent coding/non-coding sequences in our selected data set. In order to evaluate this method, we perform Fisher's linear discriminant algorithm on it and get relative satisfactory discriminant accuracies. The average accuracies of the global descriptor method (36 parameters) for the training and test sets are 97.81% and 97.49%, respectively. Finally, a comparison with Z curve methods using the same data set is undertaken. When we combine our method with the Z curve method, higher accuracies are obtained. This good performance indicates that the global descriptor method of this paper may complement the existing methods for the gene finding problem.