In designing HIV protease inhibitors as potential drugs for AIDS therapy, knowledge about what peptide sequences in polyproteins are cleavable by HIV proteases is very useful. In this article, based on the formulation that any octapeptide can be uniquely expressed as a 160-dimensional vector and the principle that the similarity of any two such vectors is associated with their correlation angle, a new method is proposed to predict the cleavability of a peptide sequence by HIV-1 and HIV-2 proteases. The average predicted accuracy the new method for the 105 peptide sequences whose cleavability by HIV-1 protease is known is 96/105 = 9.14%, which is about 8% higher than that by the existing method for the same set of data. A considerably high rate of correct prediction was also obtained when the new method was used to predict the HIV-2 protease-cleaved sites in some proteins.