This paper presents an efficient algorithm for generating cutter paths for the NC milling of arbitrary pockets with multiple islands. In this algorithm, the pocket border and island profiles are made up of concave or convex segments comprising linear and circular arc elements. For the generation of NC tool paths, the algorithm is divided into four stages, namely, profile pre-processing stage, offset calculation, determination of the termination condition, and determination of the path sequence. Compared with the other pocketing algorithms, the main aspect of this work is that the pocket border and island profiles are pre-processed in the first stage of the algorithm. Making use of contour bridges in the profile pre-processing stage, the island profiles are connected to the pocket border profile to form a closed path. This then simplifies the calculations in cutter offsets and eliminates the problem of nesting which occurs in some other pocketing algorithms.