This paper introduces our compact and lightweight patient-mounted MRI-compatible 4 degree-of-freedom (DOF) robot with an improved transmission system for MRI-guided arthrography procedures. This robot could make the traditional two-stage arthrography procedure (fluoroscopy-guided needle insertion followed by a diagnostic MRI scan) simpler by converting it to a one-stage procedure but more accurate with an optimized system. The new transmission system is proposed, using different mechanical components, to result in higher accuracy of needle insertion. The results of a recent accuracy study are reported. Experimental results show that the new system has an error of 1.7 mm in positioning the needle tip at a depth of 50 mm, which indicates high accuracy.