A new method for precisely aligning the principal axes between two birefringent fibers is presented using a Michelson interferometer and a broadband source. Angular alignment can be accomplished by measuring the interference peak value corresponding to the rotation angle between the principal axes of the birefringent fibers. Angular alignment accuracy is limited by the mode coupling produced near the connection with reduced dependence on the fiber crosstalk. Following the experiment, minimum angular misalignment was +/-0.086 degrees , which corresponds to -56-dB crosstalk at the connection.