We give a new set of axioms defining the concept of (B*)-plane (i.e. Minkowski plane without the tangency property) and we show that every (B*)-plane in which a condition similar to the “Fano condition” of Heise and Karzel (see [5, § 3]) holds, is a Minkowski plane over a perfect field of characteristic two. In particular, every finite (B*)-plane of even order is a Minkowski plane over a field. Consequences for strictly 3-transitive groups are derived from the preceding results; in particular, every strictly 3-transitive set of permutations of odd degree containing the identity is a protective group PGL2(GF(2 n )) over a finite field GF(2 n , for some positive integer n.