To evaluate the progression of cognitive decline in multiple sclerosis (MS) patients and the susceptibility of the Multiple Sclerosis Functional Composite (MSFC) Paced Auditory Serial Addition Test (PASAT) to change, we conducted a 1-year follow-up with a comprehensive neuropsychological examination to 19 initially cognitively impaired and 26 cognitively intact relapsing-remitting MS patients, and to 48 healthy controls. The results indicated that the cognitive performance of MS patients remained relatively stable. Healthy controls tended to perform better on most neuropsychological measures at follow-up, the same was not observed in the MS groups. PASAT showed a significant difference between the groups: the cognitively impaired group tended to deteriorate, whereas the control group and the cognitively intact group improved. The change in PASAT could not be explained by the background variables, for example, mood, quality of life, or nervousness. Therefore, the MSFC-PASAT seems to be a sensitive measure to show clinical change in the cognitive status.