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In this paper, phase-extracted (MPE) basis functions with both the traveling wave terms and the standing wave terms have been proposed to analyze the scattering from the electrically large targets. This kind of basis functions, called modified phase-extracted (MPE) basis function, can be defined on the relatively large patches and constructed with the higher order hierarchical vector basis functions. The constructing idea of the MPE basis function is first introduced. Then, their characteristics were compared with the relevant basis functions. It has been demonstrated that the MPE basis function is suitable for the scattering analysis of the perfect electric conductors (PECs) with smooth convex surfaces as well as the concave structures, such as the electrically large cavities. The numerical solutions to the electromagnetic scattering from both the convex targets and the cavity-like targets with strong mutual couplings have been given to show the capability of the MPE basis functions in the description of the complex distribution of the induced current on the PEC surfaces. Some numerical examples have been given to demonstrate the validation of this kind of basis functions.