We have used the CO J = 3-2 transition to map the extremely high velocity (EHV) gas in the bipolar outflow from the NGC 2071 infrared cluster. The EHV material (30 km s-1 < \nu - nu-0\ < 60 km s-1) is found only within 1.'5 of the source, while the high-velocity (HV: \nu - nu-0\ < 30 km s-1) outflow extends to over +/- 3' from the source. The EHV gas is well collimated, and symmetric, with sharp velocity peaks appearing at +/- 1 from the source. The EHV gas has a temperature of approximately 80 K, significantly hotter than that of the HV gas. In view of this temperature enhancement and spatial confinement, we suggest that velocity peaks occur at the working surfaces of jets. Since molecules are dissociated in shocks faster than almost-equal-to 40 km s-1, the EHV gas most likely arises from molecules re-formed behind a fast shock. The presence of a working surface in the middle of the outflow suggests that the outflowing material is reaccelerated, extending the lifetime of the flow.