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Following a line outage, the fast corrective operations of transmission line switching might be used to regain N-1 security of the system without generation re-dispatch or load shedding. The problem to find feasible switching operations can be formulated as a constraint satisfaction problem (CSP). Feasibility checking, however, is difficult since changes in load flows caused by line switching operations are discontinuous, and many contingency cases need to be examined. In this paper, DC flow is considered for simplicity, and variables include binary line statuses and continuous phase angles. Security constraints for the base case, N-1, and selected N-2 cases are formulated in a unified way by using a separate set of phase angles for each case. The problem is solved by using constraint programming (CP), and a tree search procedure is developed. Since it is time consuming to handle continuous variables in the tree search, only binary variables are branched on. Once reaching a leaf node where the topology is fixed, the constraints become linear DC flow feasibility conditions and are examined by solving a linear programming problem. Effectiveness of the method is demonstrated on IEEE 30-bus and 118-bus systems.