Using mappings of the form (1 + bf)a, (1 − bf)−aand ((1 + bf)/(1 − bf))a, we get three different unit interpolation algorithms, respectively first, second and third. The second algorithm yields a unit in H ∞ with arbitrary specified left half j-plane zeros instead of arbitrary specified left half s-plane poles, as in Youla et al. (1974) and Vidyasagar (1985) with the first algorithm. The third algorithm yields a unit in H ∞ with considerably lower degree in the cases where a is required to be greater than one with either the first or second algorithm. However, by using alternative steps from the first and second algorithms judiciously, as shown by a numerical example, one can reduce the order of the unit considerably, compared with the third algorithm. The usefulness of the second algorithm in the control system context is that the closed-loop system poles can be specified arbitrarily in the LHP in a strong stabilization problem, which is the opposite to the first algorithm of Youlaet al. (1974) and Vidyasagar (1985), where the controller poles can be specified in the LHP in an arbitrary way. The second algorithm can also be used for placing the interconnected closed loop system poles in decentralized stabilization for expanding construction of large-scale systems.