We previously reported a compact magnetometer using HTS-SQUID with a rotating sample for routine testing. In this study, we have improved the detection limit of the system to detect a very weak secondary magnetic field from diamagnetic material. The system consisted of a rotating sample table, a magnet with a pick-up coil, and an HTS-SQUID. The six sample cases can be fixed to a turntable using sample arms to enable multiple-detection. By rotating the sample, the velocity of the sample passing above the pick-up coil could be increased compared to the vibrating-sample method. The pick-up coil was directly coupled to a superconducting input coil of the HTS-SQUID to transfer the detected signal to the HTS-SQUID. The HTS-SQUID attached to a sensor probe was cooled by liquid nitrogen in a Dewar vessel, which was enclosed in a bilayer magnetically shielded cylindrical box. To improve the detection limit of the magnetometer's susceptibility, the noise of the applied magnetic fields was reduced, the pick-up coil shape optimized, and the accuracy of rotation speed was increased. As a result, the signal and noise ratio was improved and the magnetometer showed a high sensitivity and accuracy.