We present the positional abilities of a humanoid manipulator based on an improved kinematical model of the human arm. This was synthesized from electro-optical measurements of healthy female and male subjects. The model possesses three joints: inner shoulder joint, outer shoulder joint and elbow joint. The first functions as the human sternoclavicular joint, the second functions as the human glenohumeral joint, and the last replicates the human humeroulnar rotation. There are three links included, the forearm and the upper arm link which are of a constant length, and the shoulder link which is expandable. Mathematical interrelations between the joint coordinates are also taken into consideration. We determined the reachability of a humanoid arm, treated its orienting redundancy in the shoulder complex and the positional redundancy in the shoulder-elbow complexes, and discussed optimum configurations in executing different tasks. The results are important for the design and control of humanoid robots, in medicine and sports.