In this paper, a new fragile watermarking algorithm for digital image is presented, which makes resolving the security and forgery problem of the digital image to be possible. The most suitable watermarking method that verifies the authentication and integrity of the digital image is the Wong's method, which invokes the hash function (MD5). The algorithm is safe because this method uses the hash function of the cryptology. The operations such as modulus, complement, shift, bitwise exclusive-or, bitwise inclusive-or are necessary for calculating the value of hash function. But, in this paper, an Arithmetic encoding method that only includes the multiplication operation is adopted. This technique prints out accumulative probability interval, which is obtained by multiplying the input symbol probability interval. In this paper, the initial probability interval is determined according to the value of the key, and the input sequence of the symbols is adjusted according to the key value so that the accumulative probability interval will depend on the key value. The integrity of the algorithm has been verified by experiment. The PSNR is above the 51.13db and the verifying time is $1/3{\sim}1/4$ of the verifying time of using the hash function (MD5), so, it can be used in the real-time system.