Electrical properties tomography (EPT) is a recently developed noninvasive technology to image the electrical conductivity and permittivity of biological tissues at Larmor frequency in magnetic resonance scanners. The absolute phase of the complex radio-frequency magnetic field (B1) is necessary for electrical property calculation. However, due to the lack of practical methods to directly measure the absolute B1 phases, current EPT techniques have been achieved with B1 phase estimation based on certain assumptions on object anatomy, coil structure and/or electromagnetic wave behavior associated with the main magnetic field, limiting EPT from a larger variety of applications. In this study, using a multi-channel transmit/receive coil, the framework of a new general approach for EPT has been introduced, which is independent on the assumptions utilized in previous studies. Using a human head model with realistic geometry, a series of computer simulations at 7 T were conducted to evaluate the proposed method under different noise levels. Results showed that the proposed method can be used to reconstruct the conductivity and permittivity images with noticeable accuracy and stability. The feasibility of this approach was further evaluated in a phantom experiment at 7 T.