In this paper, we investigated how to establish and maintain orthogonal constellation of two orbiters around a planet, taking Mars as an example. We assumed a mission where two spacecraft (S/C) will be injected into the Mars orbit simultaneously. One S/C (MOA) has a low altitude orbit, while the other (MOB) has a highly elliptical orbit. It is assumed that MOB should look down upon MOA's orbital plane at MOB's apoapsis; i.e., the two orbits should be preferably orthogonal. Such constellation can be actually required in scientific missions featuring both global and in-situ observation of Mars atmosphere, and it can also be extended to application in other celestial bodies. How to keep the orthogonal constellation under perturbations or other restrictions, and how to establish it with small fuel consumption is the main topic of this paper.