A hash chain H for a hash function hash(·) is a sequence of hash values <x_n,x_n-1,...,x₀>, where x₀ is a secret value, x_i is generated by x_i = hash(x_i-1) for 1≤ i ≤ n, and x_n is a public value. Hash values of H are disclosed gradually from x_n-1 to x₀. The correctness of a disclosed hash value x_i can be verified by checking the equation $x_n \\stackrel{?}{=} \\hash^{n-i}(x_i)$. To speed up the verification, Fischlin introduced a check-bit scheme at CT-RSA 2004. The basic idea of the check-bit scheme is to output some extra information cb, called a check-bit vector, in addition to the public value x_n, which allows each verifier to perform only a fraction of the original work according to his or her own security level. We revisit the Fischlin's check-bit scheme and show that the length of the check-bit vector cb can be reduced nearly by half. The reduced length of cb is close to the theoretic lower bound.