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In near future humanoid robots will not only be able to socialize with the human being but will also be able to replace him even in the irksome and dangerous tasks, ranging from rescuing situations to interplanetary exploration. Nowadays many researchers are engaged on this field to make the humanoid more adaptable, intelligent and representable to the dynamic environment. Designing a suitable and efficient gait for the Biped Intelligent Machine (BIM) is a complex task. In this paper a geometrical analysis is presented to identify the movements and positions of the Center of Gravity (CoG) of a humanoid system while it balancing itself in the Single Support (SS) mode. SS mode while standing on single leg is a very critical job for a bipedal system. The paper also exemplifies the results based on the proposed Geometrical Analysis Technique (GAT) which is applied on the BIOLOID humanoid system.