parameter estimation problem in neutron diffusion is investigated for a critical reactor. This case is considered as inverse to the classical criticality problem. In this work, a one-dimensional, two-group case is examined in a multiregional core. The flux distributions in a discrete basis, a multiplication factor, region wise fractional powers and group diffusion coefficients of one region are the known data of the inverse problem. It is assumed that no adjoint solution information is available. A non-iterative direct approach is developed to reconstruct nuclear parameters of each region. The numerical results for test cases are given.