Abstract: The principle of iso-probability marginal transformation was firstly introduced, and then, it was proven that the usual Rackwitz-Fiessler transformation is the first order approximation of the iso-probability marginal transfor-mation. The extended Rackwitz-Fiessler transformation was developed through the combination of the equivalent normalization principle and linearized transformation, and its defects were also pointed out. Noting that Nataf transformation is nonlinear for non-normal variables in nature, so a linearized Nataf transformation has been put forward. Furthermore, a new FORM method based on the proposed linearized Nataf transformation and iHLRF algorithm is proposed. Finally, the computing results of a numerical example are analyzed and compared between Nataf transformation’s and linearized Nataf transformation’s and extended Rackwitz-Fiessler transformation’s, respectively. The example shows that the results of structural reliability analysis based on linearized Nataf transformation convergence the ones resusting from Nataf transformation, while there are errors in the results of extended Rackwitz-Fiessler transformation by comparing with the exact ones.