The kinematics of a robot with many degrees of freedom is a very complex function. Learning this function for a large workspace with a good precision requires a huge number of training samples, i.e., robot movements. In this paper, we introduce the Kinematic Bézier Map (KB-Map), a parameterizable model without the generality of other systems but whose structure readily incorporates some of the geometric constraints of a kinematic function. In this way, the number of training samples required is drastically reduced. Moreover, the simplicity of the model reduces learning to solving a linear least squares problem. Systematic experiments have been carried out showing the excellent interpolation and extrapolation capabilities of KB-Maps and their relatively low sensitivity to noise.