Let $Leteta={eta m}m$ be an eventually constant sequence of unit vectors $eta m$ in $C^{n}$ and let $ ho$η be the pure state on $UHF_{n}$ algebra which is defined by $ hoeta(upsilon_i_1....upsilon_i_k{upsilon_{j1}}^*...{upsilon_{j1}}^*)={eta_1}^{i1}...{eta_k}^{ik}{eta_k}^{jk}...{eta_1}^{j1}$. We find infinitely many state extensions of $ hoeta$ to Cuntz algebra $O_n$ using representations and unitary operators. Also, we present theirconcrete expressions.