Differential spatial modulation (DSM) is a newly proposed differential modulation technique tailored to spatial modulation (SM), which requires no channel state information (CSI) at the receiver. DSM can offer flexible tradeoff between the reception reliability and the system complexity. In this paper, we are the first to study the adoption of DSM in a dual-hop amplify-and-forward (AF) relaying system, which consists of a two-antenna source, a single-antenna relay, and a single-antenna destination, so as to reduce the burden of channel tracking on both the relay and the destination. We derive a general upper bound on the average bit error probability (ABEP) achieved by the system. Moreover, an exact closed-form ABEP expression and the asymptotic result are provided for BPSK signaling in Rayleigh fading environment. The same system setup with the adoption of SM at the source is chosen as a benchmark for performance comparisons. Simulation results validate the analysis and reveal a 3dB signal-to-noise power ratio (SNR) penalty of the considered system compared with the benchmark.