In this paper, a new texture descriptor inspired from Completed Local Ternary Pattern (CLTP) is proposed and investigated for texture image classification task. A wavelet-CLTP (WCLTP) is proposed by integrating the CLTP with the redundant discrete wavelet transform (RDWT). Firstly, the images are decomposed using RDWT into four sub-bands. Then, the CLTP are extracted from the LL sub-bands coefficients of the image. The RDWT is selected due to its advantages. Unlike the other wavelet transform, the RDWT decompose the images into the same size sub-bands. So, the important textures in the image will be at the same spatial location in each sub-band. As a result, more accurate capturing of the local texture within RDWT domain can be done and the exact measure of local texture can be used. The proposed WCLTP is evaluated for rotation invariant texture classification task. The experimental results using CURTex and Outex texture databases show that the proposed WCLTP outperformed the CLBP and CLBC descriptors and achieved an impressive classification accuracy. Furthermore, the WCLTP outperformed the CLTP in Outex and many cases in the CURTex databases.