Certain facts about frames and generalized frames are extended for the new -frames, referred as * --frames, in a Hilbert C * -modules. As a matter of fact, some relations are establish between * -frames and * --frames in a Hilbert C * -module. Furthermore, the paper studies the operators associated to a given * --frame, the construction of new * --frames. Moreover, the operator duals for a * --frame are introduced and their properties are investigated. Finally, operator duals of a * --frame are characterized.