It is shown that Banach space X is locally uniformly non square if and only if d X(x

1)>0 for all x∈S(X) ; X is strongly strictly convex if and only if whenver for any x∈S(X)

y n∈S(X) and α∈R

if ‖x+αy n‖→0

and ‖x-αy n‖→1

then α=0 ;and X is strongly strictly convex if and only if X is midpoint locally uniformly convex.