A novel method, the discrete cones method (DCN), is proposed as an alternative to the discrete ordinates method (SN) for solutions of the two-dimensional neutron transport equation. The new method utilizes a new concept, discrete cones, which are made by participating a unit spherical surface that the direction vector of particles covers. In this method particles in a cone are simultaneously traced instead of those in discrete directions so that an anomaly of the SN method, the ray effects, can be eliminated. The DCNmethod has been formulated for X-Y geometry and a program has been created by modifying the standard SNprogram TWOTRAN-II. Our sample calculations demonstrate a strong mitigation of the ray effects without a computing cost penalty.