  A new coordinate system is defined for the Four-Body dynamical problem with
general masses, having as its origin of coordinates the center of mass. The
transformation from the inertial coordinate system involves a combination of a
rotation to the principal axis of inertia, followed by three changes of scale
leading the principal moments of inertia to yield a body with three equal
moments of inertia, and finally a second rotation that leaves unaltered the
equal moments of inertia. These three transformations yield a mass-dependent
rigid orthogonal tetrahedron of constant volume in the inertial coordinates.
Each of those three linear transformations is a function of three coordinates
that produce the nine degrees of freedom of the Four-Body problem, in a
coordinate system with the center of mass as origin. The relation between the
well known equilateral tetrahedron solution of the gravitational Four-Body
problem and the new coordinates is exhibited, and the plane case of central
configurations with four different masses is computed numerically in these
coordinates.
