In this paper, bandwidth improvement of E-plane sectionalized rectangular horn antenna is studied, which has been introduced for sidelobe level (SLL) reduction and gain improvement of traditional rectangular horn antennas. The main drawback of initial sectionalized horn antenna is the limited bandwidth. In this paper, a reason of this drawback is explained, which is the presence of phase variance of electromagnetic fields on the aperture, and a method is proposed for solving this issue, which is the modification of the phase velocity based on the equations for rectangular waveguides. Consequently, as well as modifying the field amplitudes on the aperture, the proposed method can be used for modification of the phase variance on the aperture. Based on this method, an approximately constant phase on the E-plane of the aperture is obtained. The effectiveness of this method is validated by illustrating the field distributions inside the antenna and on the aperture in simulations. Consequently, bandwidth enhancement by resolve of the initial antenna drawback at the higher frequencies, efficiency improvement without changing the antenna length, and successful measurements for validating the calculations and simulations are the main achievements of this paper. The aperture efficiency of the proposed X-band antenna is higher than 54 % for the frequencies below 11.3 GHz.