In this paper a numerical integration method termed ''μ' t fitting'' for application to the true-height analysis of digitally recorded ionograms is introduced. This method can be used to analyze either the O or X waves in an ionogram and includes the effect of the Earth's magnetic field. For the second order polynomial profile analysis the μ't fitting technique utilizes 38--62% fewer numerical operations than the Gaussian quadrature integration method. Applying 5- (12-) term μ't fitting to 100 data points, the method completes a true-height analysis in 0.77 (1.43) s, using an 80486/33 computer system. Furthermore, applying this technique to the overlapping Chapman model profile adopted by Union Radio Scientifique Internationale (URSI) Working G.6.2 (McNamara and Titheridge, 1977) yields rms errors of 8.3 and 7.0 meters for the O and X wave components (12-term μ't fitting), over a set of 22 selected frequencies. ¿ American Geophysical Union 1995