A modular hip prosthesis includes a femoral stem, a spherical head and a coupling member extending from the head defining a neck whose lower end forms a base which plugs into a socket at the top of the stem to form a tapered neck/stem junction. That junction is aligned with the stem axis and has a cross-section with opposite sides that extend generally parallel to the sides of the stem. With such an arrangement, that junction may be relatively long and have a relatively large cross-sectional area thus making a strong junction even in smaller femoral implants.