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Let \(G\) be a bipartite graph with bipartite sets \(V_1\) and \(V_2\). If \(f\) is a bijective function from the vertices and edges of \(G\) into the first \(p+q\) positive integers, where \(p\) and \(q\) denote the order and size of \(G\), respectively, meeting the properties that \(f\) is a super edge magic labeling and if the cardinal of \(V_i\) is \(p_i\) for \(i=1,2\), then the image of the set \(V_1\) is the set of the first \(p_i\) positive integers and the image of the set \(V_2\) is the set of integers from \(p_1 + 1\) up to \(p\). If a bipartite graph \(G\) admits an special super edge magic labeling, we say that \(G\) is special super edge magic. Some properties of special super edge magic graphs are presented. However, this work is mainly devoted to the study of the relations existing between super edge magic and special super edge magic labelings.