In this paper we present a new numerical scheme for the Method Of Characteristic (MOC) in unstructured geometries for the neutron transport equation. The MOC has become a familiar tool for transport calculations in reactor physics [1], and its use will probably increase in the future. One of the major drawbacks of the MOC is the difficulty to implement higher-order integration schemes to improve spatial convergence. We present here a higher-order schemes for the MOC. We define a conservative and linear characteristic scheme based on linear interpolation on the surface’s values of the collisions sources. We have called it Conservative Linear Surface (CLS) scheme in contrast to a preceding non conservative version. Results comparisons of the well-known Stepanek benchmark show CLS faster convergence over the standard step characteristic scheme. A generalization of the synthetic DPN acceleration scheme provides an efficient method to accelerate the internal transport iterations.