<p>Building upon the conditions satisfied by the double Hilbert transform, Journé introduced a class of non-convolution-type singular integral operators with product structure, now referred to as the Journé class. To investigate the boundedness of operators on multi-parameter local Hardy spaces, researchers introduced inhomogeneous Journé-type singular integral operators. Subsequent studies have demonstrated that many operators naturally fall within this inhomogeneous Journé class. Analogous to the two aforementioned classes of sets, mixed Journé class were introduced. Up to now, the question of whether the set of mixed Journé class is non-empty remains open. The primary objective of this study is to provide an affirmative response to this question.</p>