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Radial basis function (RBF) collocation method is a kind of pure meshless numerical method and has been applied to solve static and transient electromagnetic problems. Especially, it shows a great advantage in the computation of moving conductor eddy current magnetic problems. To simulate the conductor movement, the field equations are decoupled with superposition principle and solved by time-domain iteration under moving coordinate systems. One problem is that the coefficient matrix of RBF governing equations, which needs to be computed in each iteration step, is full. As the number of RBF nodes increases, the computational capacity will grow rapidly. The domain decomposition method (DDM), which divides the solving domain into several subdomains, could be conveniently combined with RBF collocation method. This paper first applies DDM combined RBF collocation method to compute transient eddy current magnetic field problems with moving conductors. With this novel method, the iteration only proceeds in the subdomains containing conductors. And the magnetic field in the subdomains without conductors needs to be computed just once before the iteration. The dimension of the coefficient matrix computed in the iteration is only determined by the number of nodes in the corresponding subdomains and on the interfaces. An engineering problem is computed to show that the DDM combined RBF collocation method is much more efficient than the normal one.