On March 19, 2009, in Tirana has ended negotiations and initialed Agreement between Greece and Albania on delimitation of continental shelf and other maritime areas belonging, according to International Law. This agreement was signed in Tirana, from two respective Ministers of Foreign Affairs, on April 27, 2009. Since its introduction, agreement states that the maritime borders between Albania and Greece, will be determined on basis of equity distance expressed by medium line. Merits of case would require study of complete file of agreement, including texts of agreement in three languages: English, Greek and English, as well as maps of agreement, which has so far has not been made public. Emphasize that Albania has ratified UNCLOS, on June 23, 2003, while Greece on July 21, 1995. This agreement was ratified by Albanian parliament, but was unapproved by Albanian Constitutional Court, arguing that conflicted with Constitution of Albania and UN Third Convention of International Law of Sea of year 1982. The paper will address importance of signing this agreement, in context of historical, economic and geopolitical, as well as losses or profits caused by its unapproval. DOI: 10.5901/ajis.2015.v4n3p143