Abstract: The rigorous proof of the relation det A^(L)=-[Π_i=1^L q_iⁱ](1+q₁f_L(q₁,q₂,…,q_L))is given. This relation has been used to obtain the exact critical surface and the correlation length exponents of the one-dimensional directed bond percolation problem with bonds connecting 1~Lth nearest neighbours. A^(L) is related to the transfer-matrix by (7). q_i is related to the occupation probability of the i-th nearest neighbour bond p_i by q_i=1-p_i (i=1, 2, …, L). f_L is a multi-varlable polynomial in q_i's.