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The least concave majorant, $\widehat{F}$, of a continuous function $F$ on a closed interval, $I$, is defined by $$\widehat{F}\left(x\right)=inf\{G\left(x\right):G\ge F,G\text{concave}\},x\in I.$$ We present an algorithm, in the spirit of the Jarvis March, to approximate the least concave majorant of a differentiable piecewise polynomial function of degree at most three on $I$. Given any function $F\in {𝒞}^4\left(I\right)$, it can be well-approximated on $I$ by a clamped cubic spline $S$. We show that $\widehat{S}$ is then a good approximation to $\widehat{F}$. We give two examples, one to illustrate, the other to apply our algorithm.