There are two types of composition systems for the Korean alphabet: a combined system and a composite system. This paper decribes an efficient coding method for both of these two types. Using this coding method with the combined system yields about 10.5% code-length savings per a Korean character while it yields about 45% savings with the composite system. In other words the coding method produces a better result(i.e. 34.5% better) with the composite system than with the combined system. The simulation has been performed on a MasPar machine having 64 processors. The results show that the combined system achieved a 45.851-fold speedup while the composite system achieved a 47.274-fold speedup.