This paper proposes an approach for examining the small-signal stability of transmission power grids in presence of a power line removal. Employing this approach, we derive an algebraic certificate for directly checking the existence of a new stable equilibrium point after the outage of a power line. This criterion is obtained based on the power network structure and power flow parameters without requiring the inertia parameters of generators, calculating the new equilibrium point, and the linearization technique. Therefore, the computational cost is much less than that of the well-known eigenvalue analysis approach for evaluating the small-signal stability of power systems, and the derived certificate gives insights into the power system's structure and parameters for achieving stability. A numerical test is then introduced to illustrate the proposed method.