Definition 1 ($MIF(k)$): A maximal intersecting family of k-sets [in short $MIF(k)$] is uniform intersecting family of k-sets such that if a k-set is not a member of family then there is at least a member in the family which has no common member with that k-set.
Definition 2 ($ISP(k)$): An intersecting family of k-sets say $(P, \mathbb B, \in)$ such that for each $B \in \mathbb B$ there exists a (k-1)-set $A^{'}$ such that $B$ and $A^{'}$ has no common element and $A^{'}$ intersects all the blocks except $B$.
Is it true that any $MIF(k)$ contains an $ISP(k)$ with the same point set $P$?