The Problem of finding the roots (eigenvalues) of the equation det A(λ)=0, where A in an n×n matrix, is studied. There exist several efficient local iterative methods for this problem. However, no efficient global method is available. We describe the application of the continuation method to this problem and solve two examples by it. We conclude that the continuation method is a practical global strategy for locating eigenvalues of non-linear matrices. This method is even more effective when it is combined with an appropriate iterative scheme.