In this paper we consider mappings ${sigma}$ which map the binary operation symbol f to the term ${sigma}$(f) which do not necessarily preserve the arities. We call these mappings generalized hypersubstitutions. Any generalized hypersubstitution ${sigma}$ can be extended to a mapping $hat{sigma}$ on the set of all terms of type ${ au}$ = (2). We de ne a binary operation on the set $Hyp_G$(2) of all generalized hypersubstitutions of type ${ au}$ = (2) by using this extension The set $Hyp_G$(2) together with the identity generalized hypersubstitution ${sigma}_{id}$ which maps f to the term f($x_1,x_2$) forms a monoid. We determine all regular elements of this monoid.