By introducing parameters with local information, several types of orthogonal moments have recently been developed for the extraction of local features in an image. But with the existing orthogonal moments, local features cannot be well-controlled with these parameters. The reason lies in that zeros distribution of these moments’ basis function cannot be well-adjusted by the introduced parameters. To overcome this obstacle, a new framework, transformed orthogonal moment (TOM), is set up. Most existing continuous orthogonal moments such as Zernike moments, fractional-order orthogonal moments (FOOMs), etc. are all special cases of TOM. To control the basis function’s zeros distribution, a novel local constructor is designed, and local orthogonal moment (LOM) is proposed. Zeros distribution of LOM’s basis function can be adjusted with parameters introduced by the designed local constructor. Consequently, locations, where local features extracted from by LOM, are more accurate than those by FOOMs. In comparison with Krawtchouk moments and Hahn moments etc., the range, where local features are extracted from by LOM, is order insensitive. Experimental results demonstrate that LOM can be utilized to extract local features in an image.