We have two mass points of equal masses m1 = m2 > 0 moving under Newton's law of gravitational attraction in a collision hyperbolic orbit while their centre of mass is at rest. We consider a third mass point, of mass m3 = 0, moving on the straight line L perpendicular to the line of motion of the first two mass points and passing through their centre of mass. Since m3 = 0, the motion of the masses m1 and m2 is not affected by the third mass and from the symmetry of the motion it is clear that m3 will remain on the line L. The hyperbolic collision rectricted three-body problem consists in describing the motion of m3. Our main result is the characterization of the global flow of this problem. © 1996 IOP Publishing Ltd and LMS Publishing Ltd.