  In this paper, we present a new ansatz for approximated solving equations of
motion of the infinitesimal mass m in case of bi-elliptic restricted problem of
four bodies (BiER4BP) (where three primaries M1, M2, M3 are rotating around
their common centre of mass on elliptic orbits with hierarchical configuration
M3 < M2 << M1). A new type of the solving procedure is implemented here to
obtain the coordinates of the infinitesimal mass m. Meanwhile, the system of
equations of motion has been successfully explored with respect to the
existence of semi-analytical (approximated) way for presentation of the
solution. We obtain as follows: 1) the solution for coordinates {x, y} = {0, 0}
is approximately satisfied both the first and second equations of motion if we
take into consideration assumption {M3, M2} << M1, 2) the expression for
coordinate z(f) is given by the equation of 2-nd order, which describes
Sitnikov-type approximated solution. It means that test particle is moving
along the z-axis, outward the common barycenter of the system (but
perpendicular to the plane of the mutual rotation of all the primaries).
