This report is composed of the following two parts and appendix. (I) Improvement of the Method for Evaluating Reactivity Based on Monte Carlo Perturbation Theory: Theoretical formulation in Monte Carlo perturbation method had been checked, and then introduced into a calculation code. There are some cases that the results of the change of eigenvalues becomes positive or negative by changing the estimator, and there is no reasonable difference in the results between the conventional method, which does not consider the change of neutron source distribution caused by a perturbation, and the new method, which consider that change. Thus it is still necessary to check the Monte Carlo perturbation code. (II) Improvement of Nodal Transport Method for 3-D Hexagonal Geometry: We can accurately evaluate hexagonal geometry FBR core by nodal transport calculation code for hexagonal-Z geometry named `NSHEX`. However it is also found that in very heterogeneous core the results is ...