B737-300
Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 233; Flight Crew Type 9000
Confusion; Human-Machine Interface
Aircraft Equipment Problem Less Severe; Deviation / Discrepancy - Procedural Published Material / Policy
Flight Crew Took Evasive Action; General Maintenance Action
Aircraft; Human Factors
While cruising at FL350; we received a TCAS RA directing a climb. The IVSI gave a green arc between 700 and 1;000 fpm climb and a red arc beyond that. The target aircraft was showing coincident with our location; however; while complying with the RA; neither pilot noticed the threat aircraft displayed on the IVSI was directly ABOVE us. (We didn't see the 'plus' symbol next to the target as it was mixed in with our aircraft symbol.) We complied with the RA and initiated a climb. We received a clear of conflict almost immediately after initiating the climb. Our altitude deviation was 100 FT to FL351 (35;100 FT.) I notified ATC of the RA and our maximum deviation. I told ATC we were clear and returning to FL350. ATC had only one other aircraft in the vicinity. Company XXX was level at his cruise altitude FL360. At the time of the RA; he was directly ABOVE us. Yet; our RA wanted a climb INTO the traffic. No other traffic was in the area and Company XXX did not get any TCAS warning either TA or RA. Upon landing at BWI; Maintenance was notified and the TCAS system was entered into the logbook as a discrepancy.  I believe this was a malfunction of the TCAS.
I reacted a little slowly but started a climb to maintain the 600 FT to 800 FT climb required by the VSI on the 737-300 and turned off the autopilot. At first; I overshot to 1;000 FT to 1;200 fpm; but reduced it to the green climb area...My slow reaction was due to looking for the directed information which is on the VSI on the 737-300 as opposed to the primary display on the 737-700.
While level at FL350 the flight crew of a B737-300 responded to an apparently aberrant TCAS 'climb' warning. The only traffic in the vicinity was a company aircraft level at FL360.