In this study, we investigate the locus of the centers of the Meusnier spheres of a space curve. Just as focal curve is the locus of the centers of the osculating spheres, we investigate the geometrical interpretation on the locus of the centers of the Meusnier spheres. We proved that if the curve is a curvature line, then the locus of the centers of the Meusnier spheres of the curve is an evolute curve. Then we give the relations between this evolute curve and the focal curve. Also, we give some relations between helices, slant helices and the locus of the centers of the Meusnier spheres of the curve.

osculating circle, osculating sphere, Meusnier sphere, evolute curve.