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The hepatocellular carcinoma (HCC) is the most frequent malignant liver tumor. The golden standard for HCC diagnosis is the needle biopsy, but this is invasive, dangerous. We aim to develop computerized, non-invasive techniques for HCC automatic diagnosis, based on the information obtained from ultrasound images. The texture is an important property of the internal body tissues, able to provide subtle information about the pathology. We previously defined the textural model of HCC, consisting in the set of the relevant textural features, appropriate for HCC characterization and in the specific values of these features. In this work, we analyze the role that the superior order Gray Level Cooccurrence Matrices (GLCM) and the Edge Orientation Cooccurrence Matrices (EOCM) have concerning the improvement of HCC characterization and automatic diagnosis. We also determine the best spatial relation between the pixels that leads to the highest performances, for the both superior order GLCM and EOCM.