Summary: The present paper gives a converse result by showing that there exists a function \(f\in C_{[-1,1]}\), which satisfies that \(\text{sgn}(x)f(x)\geq 0\) for \(x\in [-1,1]\), such that \[ \limsup_{n\to\infty} {{E_ n^{(0)}(f,1)} \over {E_ n(f)}}=+\infty, \] where \(E_ n^{(0)}(f,1)\) is the best approximation of degree \(n\) to \(f\) by polynomials which are copositive with it, that is, polynomials \(P\) with \(P(x)f(x)\geq 0\) for all \(x\in[-1,1]\), \(E_ n(f)\) is the ordinary best polynomial approximation of \(f\) of degree \(n\).