There exists a class of non-linear systems which cannot be transformed into a non-linear observer form (an observable linear system up to output injection) via diffeomorphism, but can be immersed into a higher dimensional non-linear observer form. This class of systems can be characterized by a differential equation called characteristic equation. If the system is an n dimensional system and it is immersible into n + m dimensional observer form, the characteristic equation involves n + m + 1 unknowns where n + m unknowns are for the state immersion and one for the output transformation. In general, one should solve these unknowns simultaneously which makes the characterization difficult. After investigating the algebraic structure of the characteristic equation, we present an algorithm to check the immersibility under a constant rank assumption. Using the algorithm, one can check the immersibility iteratively since only one unknown is involved at each step of the algorithm.