Maximal commutative subalgebras of the algebra of n by n matrices over a field k very rarely have dimension smaller than n. There is a (B, N)-construction which yields subalgebras of this kind. The Courter's algebra that is of this kind was shown a (B, N)-construction whereBis the Schur algebra of size 4 andN=k4. That is, the Courter's algebra is isomorphic toB⋉ (k4)2, the idealization of (k4)2. It was questioned how many isomorphism classes can be produced by varying the finitely generated faithfulB-moduleN. In this paper, we will show that the set of all algebrasB⋉N2fall into a single isomorphism class, whereBis the Schur algebra of size 4 andNa finitely generated faithfulB-module.