R. Miron [3] by means of the Sasaki lift $\overset{\circ}{G}$ introduced a new lift $G$ which is 0-homogeneous on $\widetilde{TM}=TM\backslash\{\emptyset\}$. Some geometrical properties are studied using the almost complex structure $F$ which preserves the properties of homogenity. In this paper, we similary studied the case of the cotangent bundle $\widetilde{T*M}=T*M\backslash\{\emptyset\}$ with a 0-homogeneous lift $\overset{*}{\mathbf G}$, using [5].