Abstract: Abstract：A new kind of method for constructing the rational function approximations for transcendental functions is provided. Differing from Pad′e method, the new method utilizes the conditions which the values of the transcendental function and its approximation approximate each other, less depending the Taylor expansion of the transcendental function. Taking both of transcendental functions for examples, the differences between the approximations derived with the method and Pad′e approximations are discussed. Using the method, we construct a series of approximations suitable to operate on microcontroller.