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Common-Edge signed graph CE(S) of a signed graph S is a signed graph whose vertex-set is the pairs of adjacent edges in S and two vertices are adjacent if the corresponding pairs of adjacent edges of S have exactly one edge in common, with the sign same as that of Common-Edge. S-Marked signed graph T is a signed graph which receives the marking μ due to the signed graph S called marker. Further, T is S-consistent if a marker S is defined and if S-marking μof T with respect to which marked signed graph Tμ is consistent. In this paper, we give an algorithm to detect if CE(S) is S-consistent or not and determine its complexity.• Algorithm to detect if CE(S) is S-consistent or not.• Determination of algorithm's complexity.