Objective Full-form Magnetic Resonance Electrical Properties Tomography (MREPT) requires both B1+ magnitude and phase information. Since B1+ phase can be obtained faster and with higher SNR compared to B1+ magnitude, several phase-based methods have been developed for conductivity imaging. However, phase-based methods suffer from a concave bias due to the assumption that ∇|B1+| is negligible in the ROI. Approach In this paper, we re-derive the central equation of phase-based cr-MREPT without assuming that ∇|B1+| is negligible and thus propose a correction method directly integrated into the equation system. Main Results Proposed method successfully corrects the concave bias on both simulated and experimental data and significantly increases image quality. Significance The proposed correction method depends on a very low-resolution |B1+| map, and therefore the imaging time does not increase significantly for obtaining B1+ magnitude. Moreover, correction can be achieved using simulated B1+ magnitude, hence completely removing the additional imaging requirement.