B737-400 flight crew encountered a split flap condition on approach. Executed a go around; ran appropriate checklists and returned for a safe landing.

Narrative

On short final we had a flap malfunction. We were around 1300 MSL when I called for Flaps 30. At that point; both of us noticed that the flaps had not gone from 15 to 25 when the Captain put the lever to 25; and we noticed a split between the two needles of about one needle width. The Captain initially put the flap handle back to 15 and I checked to ensure I was still at a safe speed for that flap setting. Because we were so close to landing and I knew we had several checklists to accomplish for this malfunction; I suggested we just go around and take care of those things elsewhere. The Captain agreed; and we began the missed approach. Because we were below 2000 ft. AGL and had already captured the approach mode; I reverted to level 1 automation and did a gentle; manual go-around. The Captain advised the Tower; who told us to fly the published missed approach procedure. After completing the preliminary checklists and advising the passengers; flight attendants; Approach; and Dispatch of the situation; we proceeded back to the airport to land. We decided to attempt to lower the flaps again on the next approach due to the high landing speeds associated with what would have been a flaps 10 approach. On this second approach; we began our configuration a little early so we could carefully monitor the flap extension. They extended normally through 15 this time; but between 15 and 25; and between 25 and 30; the indicator split somewhat (less than a needle width); but after reaching flaps 25 and 30 the indicators eventually matched up again after about 10 to 15 seconds. With the flaps extended to 30; we completed the approach and landing uneventfully. The emergency equipment followed us back to the ramp and we wrote the plane up and gave it to maintenance for follow-up.