In this paper, a special kind of n-ary terms of type n, which are called T(n; Y )-full terms, are introduced. They are derived by applying transformations on the set n = f1; 2; : : : ; ng with restricted range. Under the superposition operation Sn, the algebra of such terms called the clone of T(n; Y )-full terms is constructed. We prove that the superassociative law is satisfied in the clone of T(n; Y )-full terms and the freeness is investigated using a generating set and a suitable homomorphism. Based on the theory of hypervariety, we study T(n; Y )-full hypersubstitutions which are maps taking all operation symbols to our obtained terms. These lead us to provide the classes of T(n; Y )-full hyperidentities and T(n; Y )-full solid varieties. A connection between identities in cloneT(n;Y )(n) and T(n; Y )-full hyperidentities is established.