This paper presents a novel approach for algorithmic singularity avoidance for reactionless visual servoing of a satellite mounted space robot. Task priority approach is used to perform visual servoing while reactionless manipulation of the space robot. Algorithmic singularity is prominent in such cases of prioritizing two tasks. The algorithmic singularity is different from the kinematic and dynamic singularities as the former is an artefact of the tasks at hand, and difficult to predict. In this paper, we present a geometric interpretation of its occurrence, and propose a method to avoid it. The method involves path planning in image space, and generates a sequence of images that guides the robot towards goal avoiding algorithmic singularity. The method is illustrated through numerical studies on a 6-DOF planar dual-arm robot mounted on a service satellite. © 2015 IEEE.