The generalization of spherical rectification theory was considered to spatial RCCC linkages to visit four given positions. The problem of synthesis of spatial four-bar linkages of the RCCC type for rigid-body guidance with four given positions was focused, in which R denoting a revolute, C denoting a cylindrical kinematic pair. While synthesis equations for CC and RC dyads were available in literatures, the synthesis of spatial RCCC four-bar linkages required special attention due to its asymmetric topology. However, infinitely many exact solutions to the problem of CC-dyad synthesis existed for the four-pose rigid-body-guidance problem, the RC-dyad synthesis admitted only approximate solutions, thus the RCCC linkage was capable of visiting four positions. A solution region theory was proposed to synthesis a RCCC linkage which was to visit four positions. Firstly, the expression of spherical Burmester curve and the classification was given to make a solution region. The second solution region (moment solution region) was born follow-up by picking a point on Burmenster curve solution region. Secondly, the second region which also was the spatial 4C linkage solution region, while the linkage was 2-DOF. Through restricting the prismatic joint between drive and ground on spatial 4C linkage solution region, a spatial RCCC linkage which can visit four given positions was got. Finally, two examples were given which proved that the theory was validated and correct.