A new second order method (CDSN-method) for solving the transport equation is developed. This method takes into consideration a local property of the transport equation solution in each mesh cell. Every cell is divided into three subdomains by two characteristic lines intersecting the vertices. In each subdomain the solution is a smooth function, if incident fluxes are smooth. This allows us to construct a new algorithm. Taking into account the linear character of the transport equation, its solution in every cell may be considered to be a sum of two solutions. One of them is a solution depending on boundary radiation and a zero spatial source (E–component). The other is a solution depending on a spatial source and zero boundary radiation (S–component). Different combined methods were obtained by using various algorithms for construction of E–and S–components.