It has been pointed out that the solutions in a latent class analysis are seriously unstable. There seems to exist two causes of the instability. One is a geometric structure in a latent class model and the other is a property of the methods for solving the latent structure equations. In the latter there are several methods that have been proposed so far. A robust method which copes with the instability of the model, however, has not, yet been proposed. In this paper we will only treat the latent class analysis with two classes. The aim is to suggest a criterion on the choice of a left signature and a stratifier of Gibson's method, so that the method may become a robust one. Moreover in order to get highly reliable solutions we shall give a new proposal to develop items, i.e., questionnaire. A numerical example will be given.