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By using the Newton-Raphson method to solve a quartic equation of the Lagrange parameter, we propose a new iterative algorithm for the transformation from Cartesian to geodetic coordinates. Numerical experiments show that the new method is sufficiently precise and free from singularity and non-convergency, except within 50km of the geocentre. After one iteration, the maximum error of latitude is less than 10^-^8arc-sec and the relative height error is less than 10^-^1^5 over the range of geodetic heights from -10^6 to 10^1^2m. Comparisons of the complexity and performance with some other well-known methods indicate that the algorithm is efficient and accurate.