A classification of Bernstein algebras in dimensions n ⩽ 4 has been made by Holgate in [2], however that article contains no classification up to isomorphism, the problem is solved by Lyubich in [4] when K =RorC, and by Cortes [1] in the general case. Also Lyubich has given in [5] a classification of the regular nonexceptional Bernstein algebra of type (3,n−3) and a classification but not up to isomorphism of nonregular nonexceptional Bernstein algebras of type (3,n − 3) when K =C. The aim of this paper it to characterize, up to isomorphism, Bernstein algebras of type(2, n − 2) and nonexceptional of type(3, n −3) over a infinite commutative field K whose characteristic is different from 2.