We generalize the entanglement swapping scheme originally proposed for two pairs of qubits to an arbitrary number q of systems composed from an arbitrary number mj​ of qudits. Each of the system is supposed to be prepared in a maximally entangled state of mj​ qudits, while different systems are not correlated at all. We show that when a set ∑j=1q​aj​ particles (from each of the q systems aj​ particles are measured) are subjected to a generalized Bell-type measurement, the resulting set of ∑j=1q​(mj​−aj​) particles will collapse into a maximally entangled state