The relationship between the total template dependencies and the total join dependencies is probed into by means of abstract algebra. First, two equ ivalence relations are defined in the set of the total template dependencies and the set of the total join dependencies respectively. The equivalence relations regard the dependencies that function is the same as equivalent dependencies. Th en, it is proved that two quotient sets under two equivalence relations constitute monoids respectively and there is an isomorphism mapping between the monoids, which shows that the class of the total join dependencies is essentially identical with the class of the total template dependencies. Finally, an interesting result about the total acyclic join dependencies is given. The relevant results will play active role in designing relational database schemes.