The chaotic synchronization in a one-way coupled oscillator array is studied. We find that, in certain coupling schemes (for example, the variable y driving x in the Lorenz system) and under proper coupling strengths, a nonlocal approximate synchronization happens between the first and the third oscillator, or all succeeding ones, which are not directly connected, accompanied with a desynchronization between the first and the closest, namely the second one. More detailed observation finds that under sufficiently strong coupling, there exists a single-driving-signal (not all three variables) synchronization between the first and the second oscillator that transfers the synchronization information to all remaining oscillators in the array. The nonlocal synchronization is a general phenomenon that has been observed in other systems.