Many character recognition methods use a thinning stage which facilitates shape analysis and stroke identification. There are several thinning algorithms reported in the literature of OCR. Odia, one of the Indian languages, has structurally different scripts than other Indian languages. Unlike in other Indian scripts, there has not been any special effort by OCR researchers to develop recognition techniques of this unique structural character set. In this paper, some major thinning algorithms are examined with Odia character set and show that these algorithms exhibit some sort of deficiencies when applied to Odia characters and the vital features of the character is not retained in the process. We propose a new parallel thinning technique that preserves all important features of the script.