In general, a digital watermark technique must satisfy that the embedded watermark is difficult for an attacker to remove. In this paper, we study a DWT-based watermarking scheme by Inoue et al. [9] and show their scheme is insecure. Our attack consists of two stages: In the first stage, we show that the watermark can be detected by finding the position of zerotree's root after the wavelet transform of the watermarked image. Then in the second stage, we show the embedded watermark can be removed or replaced. In this paper, we also propose an improved method of digital watermark. Simulation results show the proposed method is robust against various signal-processing attacks.