Fast healing of the network is as a main concern for remedial action that can prevent cascade tripping of the power system. Lack of practical solutions makes it difficult to heal the network as fast as possible. This article proposes a fast and intelligent method to heal the network from unstable conditions, thereby preventing power system cascade tripping and blackouts. At first, a method is proposed to centrally detect unstable synchronous machine(s) that should be isolated from the network. Then, the loads that should be shed are selected in an intelligent approach. Accordingly, the loads that have more influence on oscillation damping are selected for load shedding. Finally, a very fast convex optimization method, as an advanced computational tool, is applied on a non-linear power system to define the number of loads that should be shed. Using this method prevents network oscillation from being damped considerably fast, and transmission lines overloading is prevented after large generation outage, which in turn can prevent protection relays maloperation. The effectiveness of the proposed methods is investigated on a 39-bus New England system, and corresponding results are presented.