Elliptical signal model for bSSFP imaging has found various applications such as banding artifact removal and quantitative mapping of physical parameters. Typically, four or more phase-cycled acquisitions are needed and thus impose a limiting factor in term of total scan time. In this work, it is found that the phase-cycled bSSFP system can be unlocked using a general analytical solution with only three acquisitions, leading to a significant reduction of total scan time. Mathematical frame work is presented, followed by validation with simulated data. Future work includes further demonstration, optimization, and applications with phantoms and in vivo subjects.