An indirect method of modelling age-specific fertility rates by a double trigonometric transformation by orthogonal polynomials of degree 4 is described and applied to Hungarian data on age specific fertility rates for 1959-80. The 1st transformation changes rates into angles. To avoid overcomplexity of the polynomials while using the new approach, the 2nd transformation changes angles into u numbers using the procedure developed by Gudermann or Lambert based on the theory of complex numbers. After the 2nd transformation, instead of calculating the ordinary trigonometric values of the angles, one can calculate the hyperbolic values of the u numbers resulting from the transformation. The results of the new method were judged by comparing the sums of the squares of the differences between the empirical rates and the adjusted rates obtained by several alternative methods. In 19 of the 22 years from 1959-80, the density function of the gamma distribution, adjusted by the direct method of moments, gave the best fit. However, for 1968, 1975 and 1980, the present procedure gave better approximations.