Fractal geometry has been widely used to characterize irregular structures. Our interest in applying this concept in biomedical research leads us to the conclusion that there are no standard methods. In order to objectively set parameters involved in the estimation of fractal dimension, a significantly more accurate and efficient box-counting method based on a new algorithm was developed. Measurements of mathematical objects with known fractal dimension was performed using the traditional method and the proposed modification. The latter always yields results with less than 1% difference from the theoretical value, which represents a significant improvement.