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The paper proposes a modification of the steganographic method of embedding a digital watermark into Wavelet transform domain of a digital image. The proposed method embeds a watermark in the high-frequency detail coefficients of a three-level Wavelet transform using the Dobeshi-43 wavelet, which ensures the high quality of the resulting stego. Stego is a result of embedding of digital watermark into container and is saved in a losses format that is caused by wide dissemination of such images due to their small size. Discrete cosine transform is applied to a digital watermark, thereby increasing the efficiency of detecting the presence of a watermark in a stego. In work the analysis of efficiency of detecting of the digital watermark depending on the threshold values defining the choice of the detailing coefficients used for embedding is carried out. A result of this analysis is establishment the fact that increase in thresholds without application of Discrete cosine transformation to the watermark leads to considerable deterioration in accuracy of detecting. Conversely, the proposed method with the threshold values Т1=80 and Т2=90 of the choice of detailing coefficients in conjunction with the Discrete Cosine Transformation of the watermark matrix increased the percentage of correctly identified stegos. The results of the experiments showed the resistance of embedding a digital watermark to compression attacks (even with image quality QF=5), imposing noise, sharpening, shifting, for which the detection accuracy averages 97%. Also, the method is resistant to scaling provided QF>50. This paper compares the resistance of the original method of embedding a digital watermark and different variations of the proposed modification of the steganographic method to complex attacks (compression in combination with other types of digital image processing). [ABSTRACT FROM AUTHOR]