Asymmetric watermarking is second generation water-marking scheme which uses different keys for watermark embedders and detectors for public applications. Recently, many algorithms to render asymmetry were suggested: for example, eigenvector watermark, periodic watermark, neural network system, etc. A simplest algorithm was proposed by Hartung and Girod. They generated a detection key by substituting noise for a portion of a given embedding key and detected the watermarks by the usual correlation test. In this paper, we generalize their idea by the concept of the angle of the two keys. We study correlation detector structure for transform based asymmetric watermarking scheme. We propose a secure transform to render asymmetry: random directional angle rotation after linear projection. We also address the merits and the drawbacks of the proposed system.