The problem discussed in this paer is to determine a nonnegative interpolating polynomial which takes the prescribed nonegative values $y_0,y_1,\cdots,y_n$ at given distinct points $x_0,x_1,\cdots,x_n$:$p(x_i)=y_i),i=0,1,\cdots,n$ this paper shows"(1) 2n is the least number of m such that there exists a polynomial $p\in P_m^{+}$ the set of all nonnegative polynomials of degree$\leq m$, satisfying the above equations for any choice of $y_i\geq 0$. (2) the above equations have a unique solution in $P_{2n}^{+} if and only if at most one of the $y_i's$ is nonzero.
