Accurate interpretation of magnetotelluric data requires an understanding of the directionality and dimensionality inherent in the data, and valid implementation of an appropriate method for removing the effects of shallow, small-scale galvanic scatterers on the data to yield responses representative of regional-scale structures. The galvanic distortion analysis approach advocated by Groom and Bailey has become the most adopted method, rightly so given that the approach decomposes the magnetotelluric impedance tensor into determinable and indeterminable parts, and tests statistically the validity of the galvanic distortion assumption. As proposed by Groom and Bailey, one must determine the appropriate frequency-independent telluric distortion parameters and geoelectric strike by fitting the seven-parameter model on a frequency-by-frequency and site-by-site basis independently. Although this approach has the attraction that one gains a more intimate understanding of the data set, it is rather time-consuming and requires repetitive application. We propose an extension to Groom-Bailey decomposition in which a global minimum is sought to determine the most appropriate strike direction and telluric distortion parameters for a range of frequencies and a set of sites. Also, we show how an analytically-derived approximate Hessian of the objective function can reduce the required computing time. We illustrate application of the analysis to two synthetic data sets and to real data. Finally, we show how the analysis can be extended to cover the case of frequency-dependent distortion caused by the magnetic effects of the galvanic charges.