Let M be a smooth closed Riemannian manifold with metric \(\rho\). Consider a system \(dx/dt=X(x,t)\) where \(x\in M\) and X(x,t) is periodic with respect to t. It is supposed that the nonwandering set \(\Omega\) is hyperbolic. For \((x_ 0,t_ 0)\in\Omega \) denote by \(W^ s(x_ 0,t_ 0)\) and \(W^ u(x_ 0,t_ 0)\) the stable and unstable manifolds respectively. It is supposed also that stable and unstable manifolds of nonwandering points intersect transversally. The author proves the following theorem. There exist \(\eta >0\) and \(\alpha >0\) such that for any \(\epsilon >0\) there exists \(\delta >0\) with the following property. If \((x_ 0,t_ 0),(x_ 1,t_ 1)\in\Omega \) and there exist \((\bar x_ 0,t)\in W^ u(x_ 0,t_ 0)\), \((\bar x_ 1,t)\in W^ s(x_ 1,t_ 1)\) with \(\rho(\bar x_ 0,\bar x_ 1)<\delta\) then there exist smooth discs \(D_ 0\subset W^ u(x_ 0,t_ 0)\), \(D_ 1\subset W^ s(x_ 1,t_ 1)\) of radius \(\eta\) centered at \(\bar x_ 0,\bar x_ 1\) and a point \(\xi\) such that \(\rho(\xi,\bar x_ 0)<\epsilon\), \(D_ 0\) and \(D_ 1\) intersect transversally at \(\xi\) and the angle between their tangent spaces at \(\xi\) is more than \(\alpha\).