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In this paper, the time domain integral equation is solved by marching-on-in-degree method with near-orthogonal higher order hierarchical Legendre basis as spatial basis functions and causal weighted Laguerre polynomials as temporal basis functions. In the traditional marching-on-in-degree solver of time domain integral equation, RWG basis functions are used as spatial basis functions. The memory requirement and time consuming is very large, which becomes a bottleneck of marching-on-in-degree method. In order to solve this problem, the object is meshed with second-order nine-node curved quadrilateral elements and near-orthogonal higher order hierarchical Legendre basis functions are adopted as spatial basis functions. Numerical results show that this method can greatly reduce the unknowns of the problem, by which it can save memory and CPU time.