An inversion code of Stokes line profiles is presented. It allows the recovery of the stratification of the temperature, the magnetic field vector, and the line of sight velocity through the atmosphere, and the micro- and macroturbulence velocities - which are assumed to be constant with depth. It is based on the response functions, which enter a Marquardt nonlinear least-squares algorithm in a natural way. Response functions are calculated at the same time as the full radiative transfer equation for polarized light is integrated. This enables us to obtain values of many free parameters in a reasonable computation time. Many numerical experiments have been performed in order to check the behavior of the code. These experiments reveal the high stability, accuracy, and uniqueness of the results, even when simulated observations present signal-to-noise ratios of the order of the lowest acceptable values in real observations.