We present a method of kinematic analysis of proper motions by vector spherical functions, and the results of its application to astrometric data. The sets of vector spherical functions which are orthonormal on a full sphere as well as on a latitude zone are constructed. Decomposition of the proper motions into a set of such functions allows model-independent study of stellar kinematics. If needed, the parameters of the standard (say, Ogorodnikov-Milne) model may be derived from the coefficients of the decomposition. In contrast to the commonly used least squares estimation of the model’s parameters, vector spherical functions identify all systematic components of the velocity field (no matter, whether they are incorporated into the model or not) and give us a possibility to test whether the data are compatible with the model. In this paper, we apply this technique for the first time to the proper motions from the UCAC4 catalog for stars in the 11 to 16 magnitude range. We derive all-sky solutions and the sol