We consider the two-cell two-hop multiple-input–multiple-output interference channel with half-duplex relays, where each source group having $M$ single antenna users communicates with the corresponding destination with $M$ antennas via two relays, each having $M$ antennas. For such a channel, by exploiting three time slots, the previously known achievable degrees of freedom (DoF) is $2M/3$ regardless of whether the half-duplex relays have global channel state information (CSI) for the first hop. In this paper, we show that using $n\geq 3$ time slots, the achievable DoF is $(n-1)M/n$ , which is higher than the previous result of $2M/3$ DoF for the case of $n\geq 4$ . The achievability is shown by a new relaying protocol, which combines the alternate transmission strategy with an interference cancellation technique. A major implication of the derived result is that a normalized DoF of one can be achieved asymptotically without requiring global CSI at the source and relay nodes.