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This letter presents an efficient numerical method to determine the observable islands and additional measurements for placement, in an unobservable system. This is accomplished in a noniterative manner via the use of the Echelon form of a reduced order measurement Jacobian matrix, that is associated with a subset of the injection measurements and a subnetwork of the entire system. The proposed method is faster and easier to implement than existing approaches and gives more reliable results due to better conditioning of the processed matrices. The IEEE 14-bus system illustrates the steps of the proposed method.