Automatic bank check processing is a very hard task as it requires efficiency and precision. Banks have been adding different background patterns in the checks to increase its security. For automatic recognition of the contents of the check, the systems need to remove this background as it does not contain any valid information of the check. This can be done by thresholding algorithms which can work in document images removing all the background and letting just the ink colors to remain. In this paper, we present a new algorithm to threshold images of the courtesy amount of Brazilian bank checks. This new algorithm uses the concept of entropy as defined by Tsallis to find the best cut-off value. Experiments have shown that our algorithm is better than several well-known thresholding algorithms.