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We first define a new monoid construction (called unified-like product $O{\diamond }_{\Omega }J$) under a unified product $O\bowtie J$ and the Schützenberger product $O\diamond J$. We investigate whether this algebraic construction defined with operations of the unified and Schützenberger product specifies a monoid or not. Then, we obtain a presentation of this new product for any two monoids. Finally, we define the necessary and sufficient conditions for $O{\diamond }_{\Omega }J$ to be regular.