We derive a rigorous bound on the form factor $f_{+}\mathrm{}\left(0\right)\mathrm{}$ in the form $\left|f_{+}\mathrm{}\right(0\left)\right|\le [\frac{16}{(m_K-m_{\pi })}\times (\sqrt{m_K}+\sqrt{m_{\pi }}\left)\right]$${\left[\frac{\pi \Delta \mathrm{}\left(0\right)\mathrm{}}{3(m_K+m_{\pi })}\right]}^{\frac{1}{2}}$, where $\Delta \mathrm{}\left(0\right)\mathrm{}$ is the propagator of the divergence of the strangeness-changing current at zero momentum transfer. Using the estimate of Mathur and Okubo for $\Delta \mathrm{}\left(0\right)\mathrm{}$, we get $\left|f_{+}\mathrm{}\right(0\left)\right|\le 1.0$ and $\left|\frac{f_K}{f_{\pi }}\right|\le 1.28$.

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