Both the clear effects and minimum aberration criteria are the important rules for the design selection. In this paper, it is proved that some 2IVm−p designs have weak minimum aberration, by considering the number of clear two-factor interactions in the designs. And some conditions are provided, under which a 2IVm−p design can have the maximum number of clear two-factor interactions and weak minimum aberration at the same time. Some weak minimum aberration 2IVm−p designs are provided for illustrations and two nonisomorphic weak minimum aberration 2IV13−6 designs are constructed at the end of this paper.