This paper attempts to address the conflict that arises from the simultaneous implementation of state sovereignty laws and universal Jus Cogens laws within the framework of the United Nations Security Council. As a multilateral platform with membership from 193 of 196 world nations, the rules of non-intervention and sovereign equality are paramount to within the framework of the UN Security Council. However, the Security Council also espouses the sovereignty limiting rules that give it the prerogative to prohibit human rights violations such as genocide and crimes against humanity. Using the 1994 UN Resolutions 929, 933 and 934, this paper attempts to establish how the interests of the permanent members of the Security Council played a role in the decision making process, due to the ambiguity arising from the simultaneous application of two fundamentally conflicting international laws.