Define the incremental fractional Brownian field Z(H)(tau, S) = B-H (S+tau) By (S), H E (0, 1), where B-H(s) is a standard fractional Brownian motion with Hurst index H is an element of (0, 1). In this paper we derive the exact asymptotic behaviour of the maximum M-H (T) = max((tau,s)is an element of[0,1]x[0,T]) Z(H(tau, S)) for any H is an element of (0,1/2) complimenting thus the result of Zholud (2008) which establishes the exact tail asymptotic behaviour of M-1/2 (T).