We propose a new asymmetric watermarking scheme. In the proposed scheme, two linear transformation matrices are constructed. One matrix is secret and applied to a secret watermark to form a public asymmetric watermark. The other matrix is public and non-full rank, which is used to perform a public (asymmetric) detection using a correlation test. Theory analysis and simulation results show that the proposed scheme not only can provide a reliable asymmetric detection, but also ensures that the embedded watermark can be detected even if the asymmetric detection is disabled.