By applying an original technique, an investigation has been carried out to determine the orientation of collagen fibrils at the boundary between two successive lamellae in alternate osteons. Evidence is reported that the predominant fiber direction does not change abruptly from one lamella to the next; there is an intermediate system of criss-crossed fibers whose main orientation makes an angle of nearly 45° with the direction of the fibers in the two adjacent lamellae. Taking a composite orthogonally reinforced laminate as a model, a mechanical interpretation of this intermediate system of collagen fibers is given.