A new method to derive linear models of the axisymmetric plasma dynamic is detailed. The method follows the modified inductance approach but adopts a different set of independent variables to perturb the equilibrium. This different basis permits one to reduce the numerical computation of the model and has revealed an interesting property of the inverse inductance matrix whose elements are influenced by the plasma only if they refer to circuits facing directly the plasma column. In terms of approximations, the method proposed is equivalent to the standard modified inductance method but has the additional advantage of ensuring numerical convergence of the perturbed equilibria and therefore it allows using Picard based numerical Grad–Shafranov solvers. A linear model of the RFX-mod machine was derived with this approach and it was validated against the experiment.