In a concentrating solar power system, many heliostats are required to concentrate incident sunlight to a receiver placed at the top of a central tower. Each heliostat consists of mirrors and two rotation axes, and the surface normal of each mirror is controlled by rotations around these axes so that sunlight is reflected toward the receiver. The first axis g is fixed to the ground, and the second axis h is attached to g. The surface normal of each mirror being attached to h is controlled by a rotation around h that is rotated around g. In addition to the most widely used configuration where g is perpendicular to the horizontal plane, another class called target-aligned or spinning-elevation type has also been considered, where g is oriented toward a target in order to achieve higher concentration. Following the approach of the target-aligned heliostat, another method is considered in this paper to exploit the orientation of the first axis taking into account the position of the receiver relative to the heliostat. It is found that by an appropriate choice of the orientation of the axis, (1) it is possible to eliminate rotation of a concentrated spot of sunlight formed on the receiver, and (2) the path of rotating mirrors of a heliostat being observed from the receiver can be made almost parallel to the row of heliostats including itself. Definitions of these heliostats and derivations of their properties are described in this paper together with several results of numerical experiments. (C) 2014 Elsevier Ltd. All rights reserved.