This paper presents a mathematical model and a methodology to solve the transmission network expansion planning problem with security constraints in full competitive market, assuming that all generation programming plans present in the system operation are known. The methodology let us find an optimal transmission network expansion plan that allows the power system to operate adequately in each one of the generation programming plans specified in the full competitive market case, including a single contingency situation with generation rescheduling using the security (n-1) criterion. In this context, the centralized expansion planning with security constraints and the expansion planning in full competitive market are subsets of the proposal presented in this paper. The model provides a solution using a genetic algorithm designed to efficiently solve the reliable expansion planning in full competitive market. The results obtained for several known systems from the literature show the excellent performance of the proposed methodology.