We have designed a prototype single-layer second-order high-T/sub c/ SQUID gradiometer that detects the transverse field gradient, and balanced the device by adopting a step-down method. The device consists of symmetrically designed 3 parallel-connected square pickup loops that are directly coupled to the SQUID. The dimensions of side loops are 3 mm outside and 1.8 mm inside. The inner dimension of the center loop is 1 mm. Step-down balancing was achieved by varying the outer dimension of the center loop until a null response was detected under uniform fields. The uniform field was generated by a 250 mm/spl times/25 mm square coil wound on a grooved garolite tube. Deviation of the coil field along the abscissa was calculated to be less than 1/spl times/10/sup -5/ within the sample range. We have investigated response of the device to field gradients along the transverse direction. Details of the design, fabrication, and results will be discussed.