The authentication is used to ensure the authentication of the owner of the data. Currently, the data is available in multimedia format viz., audio, video, image and text. The present paper focuses on the image authentication. The watermarking methods are used for the image authentication. The present paper proposes a novel method of Kurtosis based Watermarking by using Wavelet Transformation (KWWT). The proposed method uses wavelet transformation. Further, the bands or the coefficients are divided into various non overlapped windows. For each of the approximation band windows, the kurtosis value will be estimated. Then the windows in all bands will be selected based on their kurtosis value. Then, the watermark image will be embedded into the selected windows of the bands. Finally, inverse wavelet transformation will be applied to get the resultant watermarked image. The proposed KWWT method is evaluated with 14 input images and 3 watermark images. Various performance measures are estimated and the results show the efficacy of the proposed method.