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The aggregative basis functions (ABFs) are introduced to construct a size-reduced system for the marching-on-in-order (MOO) time-domain integral equation (TDIE) method to analyse transient electromagnetic scattering from conducting objects. Based on the previously developed characteristic basis function method (CBFM), a set of orthogonal vectors that expand the original unknown current coefficients are obtained via the singular value decomposition (SVD). The ABF method can be considered as an application and counterpart of CBFM in TDIE with some differences. The ABFs are aggregations of the weighted Laguerre polynomials and RWG basis functions, which are the elemental temporal and spatial basis functions, respectively. The ABFs are defined over the entire geometry and effective in each order of the MOO scheme. The proposed method gives significant reduction to matrix size and also the storage by several orders of magnitude. This is achieved because of the much less number of ABFs or the orthogonal vectors than the inner edges of the geometry. Several numerical results are presented to illustrate the validity of the proposed method.