Monitoring the follicles in women's ovaries is especially important in human reproduction. Today, the monitoring of follicles is done with human interaction. Such monitoring can be very demanding and inaccurate, and in most cases signifies additional burdens for the experts. In this paper, a new algorithm for automated computer-assisted detection of follicles in the ultrasound images of the ovary is proposed. It has a typical object recognition scheme (preprocessing, segmentation, and classification). The algorithm is based on the following idea: first, the ovary is estimated (coarsely) and then follicles are searched for. The methods used are known from literature (despeckle filter, Kirsch's operator, optimal thresholding, thinning, shape descriptions, classification), and the majority of our work was done experimenting with these methods and selecting the appropriate thresholds. The algorithm's computational complexity is of order of O(n2), which means about 6 min of processing time per an ultrasound image of dimensions of 768 x 576 pixels on HP 715 machines. It has been tested on a set of 20 real ultrasound images of the ovary. The recognition rate of follicles with these procedures was around 62%. The algorithm is not perfect, but it will be further modified and improved, as indicated in our conclusions.