We present a new algorithm for 1D magnetotelluric (MT) data inversion. It inverts a normalized impedance response function derived from the classical Cagniard impedance function. The scheme transforms the nonlinear problem of estimating layer resistivities and thicknesses into a linear problem of estimating the coefficients of power series of the new response function. This is achieved by working with a model where each layer has a thickness of constant penetration. The first coefficient of the series provides top-layer resistivity, which, in conjunction with the constant penetration parameter, then provides the layer thickness. The scheme employs a recurrence relation developed between the coefficients of the power series of two successive layers. This relation is used to continue downward and estimate the remaining layer resistivities and thicknesses. The scheme has been tested on a synthetic model and on three well-studied data sets relating to deep, intermediate, and shallow exploration.