Abstract: If n and k (n>=k) are two large positive integers, then it is quite difficult to give the value of the maximal jump number M(n,k). Brualdi and Jung gave a table about the values of M(n,k) for 1<=k<=n<=10. For k=10, n=19, we prove M(19,10)=33, which verifies that one of their conjecture about the value M(2k+1,k+1) holds for k=9 and that their another conjecture M(n,k)

Key words: (0,1)-matrix, maximal jump number, conjecture