The ascending order of entropy values of the characteristic points gives a useful tool to define categories. The mathematically possible number of orderings are 3! (if there are no secondary points), 4! (if only secondary point M exists) and 5! (if both secondary points exist), which makes it 150. There are some physical constraints including the existence of the secondary points decrease the number of possible categories to 8. The categories are to be named after the ascending order of the entropy of their characteristic points. Namely the possible 8 categories are ACZ, ACZM, AZCM, ANZCM, ANCZM, ANCMZ, ACNZM and ACNMZ. The categories (also called sequences) can be fitted into the traditional three-class classification, which makes the two classification system compatible. No working fluids have been found, which could be fitted into ACZM or ACNZM categories. Theoretical studies confirmed that these two categories may not even exist. Based on the database of NIST, the proved 6 sequences of the novel classification and their relation to the traditional one can be seen in the figure.