A systematic method to define progress variables for chemistry tabulation is presented. The method is based on a Principal Component Analysis (PCA) of species mass fractions in the composition space. Analogous to an eigenvalue analysis of the Intrinsic-Low-Dimensional-Manifold method, the present study provides a rigorous mathematical formulation for flamelet-based tabulation methods. In addition, the method yields the minimum number of linearly independent progress variables for a user-prescribed desirable accuracy. Hence, the flamelet-based tabulations created with the new approach is called Intrinsically Low-Dimensional, Flamelet Generated Manifolds (IL-FGM). This approach is used to define progress variables for sample mono-dimensional, and multi-dimensional flamelet libraries of CH4-air combustion. The results show that the flamelets are tabulated and retrieved with better accuracy using the new method than those tabulated using ad hoc progress variables. (C) 2011 The Combustion Institute. Published by Elsevier Inc. All rights reserved.