In this paper, a robust image watermarking method with one-dimensional improved S transformation is proposed which is robust against geometric distortion. This watermarking is detected by a linear frequency change. The chirp signals are used as watermarks and this type of signals is resistant to all stationary filtering methods and exhibits geometrical symmetry. In the two-dimensional Radon-Wigner transformation domain, the chirp signals used as watermarks change only its position in space/spatial-frequency distribution, after applying linear geometrical attack. But the two-dimensional Radon-Wigner transformation needs too much difficult computing. We propose a modified Gaussian window which scales with the frequency in an efficient manner to provide improved energy concentration of the S-transform. The proposed scheme can resolve the time-frequency localization in a better way than the standard S transformation. The watermark is embedded in the 1D improved S transformation domains. The watermark thus generated is invisible and performs well in test and is robust to geometrical attacks. Compared with other watermarking algorithms, this algorithm is more robust, especially against geometric distortion, while having excellent frequency properties.