On gaussian diophantine quadruples

This paper concerns with the problem of constructing gaussian diophantine quadruples with the property that the product of any two distinct gaussian integers added with 1 and 4 in turn is a perfect square. The construction of gaussian diophantine quadruple is illustrated through employing the non-zero distinct integer solutions of the system of double diophantine equations. The repetition of the above process leads to the generation of sequences of gaussian diophantine quadruples with the given property.