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A 5-gap timing RPC equipped with patterned electrodes coupled to both charge-sensitive and timing circuits yields a time accuracy of 77 ps along with a position accuracy of 38 μm. These results were obtained by calculating the straight-line fit residuals to the positions provided by a 3-layer telescope made out of identical detectors, detecting almost perpendicular cosmic-ray muons. The device may be useful for particle identification by time-of-flight, where simultaneous measurements of trajectory and time are necessary.