In this paper, we study the controllability of the Bloch equation, for an ensemble of non interacting half-spins, in a static magnetic field, with dispersion in the Larmor frequency. The control are two (time-varying) radio frequency fields which are orthogonal to the static magnetic field. This system may be seen as a prototype for infinite dimensional bilinear systems with continuous spectrum, whose controllability are not well understood.  We prove that this system is not locally exactly controllable in finite time T: in fact the states that one can be reached from a given state with small control is of infinite codimension. Jr-Shin Li and Navin Khaneja  (2006, IEEE-CDC) proved   that this control system is globally approximately controllable. However if, for example, one starts with a state with the spins all close to the North Pole (of the Bloch sphere), one  need, with Li-Khaneja's method, to go a very large number of times from the North Pole to the South Pole and come back in order to go closer to the North Pole. We propose a method to do go closer to the North Pole which requires to go only once to the South Pole. The idea is the following one. At the North Pole the linearized control systems is not controllable: roughly one can control with the linearization ``half of the state space''. Similarly, at the South Pole, one can control with the linearization at the South Pole ``half of the state space''. But it turns out that these two halves are ``complementary''. Hence starting from the North Pole,  going only once to the South Pole and then returning back to the North Pole allows the linearization to control the state  (locally).