A novel BOTDA technique for distributed sensing of the Brillouin frequency in optical fibers with cm-order spatial resolution is proposed. The technique is based upon a simple modulation scheme, requiring only a single long pump pulse for acoustic excitation, and no subsequent interrogating pulse. Instead, the desired spatial mapping of the Brillouin response is extracted by taking the derivative of the probe signal. As a result, the spatial resolution is limited by the fall-time of the pump modulation, and the phenomena of secondary “echo” signals, typically appearing in BOTDA sensing methods based upon pre-excitation, is mitigated. Experimental demonstration of the detection of a Brillouin frequency variation significantly smaller than the natural Brillouin linewidth, with a 2cm spatial resolution, is presented.