In recent years various functors on

-algebras have been introduced to the realm of

-algebras. Among them are the following. With techniques usually used in algebraic topology Brown-Douglas-Fillmore [1] created the extensiion group Ext (A) and they used it to solve various problems originated from operator theory. Then Pimsner-Popa-Voiculescu generalized these and they obtained more complete picture of Ext (Y;A). In addition there is the variant of K-theory for Banach algebras [7]. The

-group of an AF algebras has been studied more extensively. These groups have the structure of the ordered "dimension group". This dimension group classifies AF algebras completely [4]. In this note we use the

-group of the rather special class of AF algebras, the so-called UHF algebras to the classification problem. Our result says that for two UHF algebras A, and B,

(A) and

(B) are isomorphic if and only if there exist natural numbers n and m such that M

(A) and M

(B) are *-isomorphic. Our result is stronger than Elliot's earlier result (see [3], [4]). And we mention that our technique is more explicit and we do not use the order structure of

-group. (i.e., dimension group)ructure of

-group. (i.e., dimension group