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In this note, we study the $L^1-$contractive property of the solutions thescalar conservation laws, got by the method of Lax-{O}le\u{\i}nik. First, it isproved when f is merely convex and the initial data is in$L^{\infty}(\mathbb{R})$. And then, it is shown for the case when the initialdata is in $L^1(\mathbb{R})$ with the convex flux having super-linear growth.Finally, the $L^1-$contractive property is shown for the scalar conservationlaws with the initial data in $L^1(\mathbb{R})$ and the flux is"semi-super-linear". This entire note does not assume any results mentionedthrough the approach by Kruzkov.

A Note on $L^1-$contractive property of the solutions of the scalar conservation laws through the method by Lax-Ole\u{\i}nik