In this paper, we demonstrated, through experiment and numerical reconstruction, that the bias and the conjugate image, which are main drawbacks in incoherent holography, can be removed. By using wave plates of the modified triangular interferometer, which was made by adding simple passive devices to the conventional triangular interferometer, we adjusted the relative phase differences of two optical waves traveling in clockwise and counterclockwise. In this way, we obtained four intensity patterns, and then by manipulating the four intensity patterns electronically we obtained the complex hologram without bias and the conjugate image. Comparing numerical reconstruction results of the complex hologram with numerical reconstruction results of the hologram obtained from the conventional triangular interferometer, we demonstrated that bias and the conjugate image can be removed using the modified triangular interferometer.