Summary: We consider the standard map. The stable and unstable manifolds of the saddle fixed point are proved to intersect transversely at the primary homoclinic point \(u\) for any parameter value. For the proof, we use the particular objects called the dominant axis (DA) and subdominant axis (SD), and symmetric periodic orbits that have orbital points on these axes. The periodic orbit named \(1/q\)-BE has the orbital point \(z_k\) at the intersection point of DA and SD. Let \(\xi_k\) be the slope of SD at \(z_k\). Take a sequence of \(z_k\) accumulating at \(u\) as \(k \rightarrow \infty \). We prove that the slope \(\xi_{} k\) monotonically decreases to the slope \(\xi_{} u(u)\) of the unstable manifold at \(u\) (the monotone inclination property). Using Ushiki's theorem, the hyperbolic region (HR) is constructed. It is proved that the orbital point \(z_k\) in HR is a saddle point with reflection. Using the monotone inclination property and the properties of \(z_k\) in HR, the transversality at \(u\) for any value of \(a (> 0)\) is proved.