In 2000, K. Denecke and K. Mahdavi showed that there are many idempotent elements in $Hyp_{N_{varphi}}(V)$ the set of normal form hypersubstitutions of type ${ au}=(2)$ which are not idempotent elements in Hyp(2) the set of all hypersubstitutions of type ${ au}=(2)$. They considered in which varieties, idempotent elements of Hyp(2) are idempotent elements of $Hyp_{N_{varphi}}(V)$. In this paper, we study the similar problems on the set of all generalized hypersubstitutions of type ${ au}=(2)$ and the set of all normal form generalize hypersubstitutions of type ${ au}=(2)$ and determine the order of normal form generalize hypersubstitutions of type ${ au}=(2)$.