In this paper, a new offset algorithm for closed 2D lines with islands is introduced and the result is illustrated. The main point of the proposed algorithm is that every point is set to be an offset by using bisectors, and then invalid offset lines, which are not to be participated in offsets, are detected in advance and handled with an invalid offset edge handling algorithm. As a result, raw offset lines without local invalid loops are generated. The proposed offset method is proved to be robust and simple, moreover, has a near O(n) time complexity, where n denotes the number of input lines. In addition, the proposed algorithm has been implemented and tested with 2D lines of various shapes.