The aim of this talk is to construct Calabi--Yau 4-folds as crepant resolution of the quotients of a hyperaehler 4-fold $X$ by a non-symplectic involution $\alpha$. First, we compute the Hodge numbers of a Calabi--Yau constructed in this way in a general setting and then we apply the results to several specific examples of  non-symplectic involution, producing Calabi--Yau 4-folds with different Hodge diamond. Then, we restrict ourselves to the case where $X$ is the Hilbert scheme of two points on a K3 surface $S$ and the involution $\alpha$ is induced by a non-symplectic involution on the K3 surface. In this case we compare the Calabi--Yau 4-fold $Y_S$, which is the crepant resolution of $X/\alpha$, with the Calabi--Yau 4-fold $Z_S$, constructed by the Borcea--Voisin construction by $S$, describing a rational $2:1$ map from $Z_S$ to $Y_S$. This is a joint work with Chiara Camere and Giovanni Mongardi.