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A new approach for a global sensitivity analysis of nonlinear mathematical models is presented using the information provided by two complementing variance-based methods. As a first step, the model is evaluated applying a shared sampling strategy for both methods based on Sobol's quasi-random sequences. Then, total sensitivity indices are estimated in a second step using the Sobol'-Saltelli method whereas first-order sensitivity indices are concurrently computed using a modified version of the well-known Fourier Amplitude Sensitivity Test. Although the analysis is focused on the calculation of total sensitivity indices, first-order sensitivity indices and thus information about the main effects of model input parameters can be obtained at no extra computational cost. Another advantage of this approach is that data of previous model evaluations can be reused for a new, more precise sensitivity analysis. The capability and performance of the method is investigated using an analytical test function.