To reduce the error of coordinate transformation, a fractional order convex valued neural network (FCVNN) is explored. The convergence is proved. We take the longitude as the real part of the input, and take the latitude as the imaginary part of the input. Thus, we construct the complex valued input of the CVNN. All longitudes and latitudes on the earth are perpendicular to each other. This satisfies that the real part and imaginary part of the complex form an orthogonal unit basis. Input Xiamen 92 space coordinates and WGS-84 space coordinates obtained from the transformation as the training samples. The weights of neural network are updated. Input the geodetic coordinates of test data and output the geodetic coordinates of WGS84 corresponding to the results. FCVNN is applied to Xiamen 92 coordinate transformation, and the transformation accuracy is improved. Using the orthogonality of longitude and latitude, CVNN are constructively used to solve the coordinate transformation problem. Many insights can be transferred from real domain to complex domain. If the data exists naturally in the complex domain, or can be meaningfully moved to the complex plane, the complex neural network should be used for the task.