This paper describes a new way of constructing a visuomotor map that is applied in a manipulator robot to accomplish a ballistic reaching task. Ballistic reaching is employed to move the robot hand to a visible and optimal position, once the robot arrives to this position a visually guided task (visual servoing or a manipulation task) could be executed. The visuomotor map has been implemented using SOM (Self-Organized Map) neural networks in a simulated puma 560 robot. The visuomotor map deals with the visibility of the robot hand (end-effector) problem. So the robot can start with its end-effector in any random position of the workspace. A Cartesian controller triggered by a visuomotor map will find a suitable and visible position for the endeffector. Results and simulations are shown to demonstrate the applicability of our proposed model for a ballistic reaching task.