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A method of constructing canonoid transformations with respect to a Hamiltonian is presented. First, the Hamiltonian system is transformed into a Birkhoffian system. Second, the Birkhoffian system is transformed into a new one under gauge transformation. Finally, the Hamiltonization of new Birkhoffian system is realized. It is pointed out that there exist many different canonoid transformations for one Hamiltonian system. Two examples are given to illustrate the application of the results.
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