B767 Captain experiences FMC CDU screen failure on a transatlantic flight. After informing ATC flight continues to destination using remaining FMC and three functional IRU's.

Narrative

After passing 20 degrees West; we both saw the right FMC screen lose data display and screen covered with straight lines. The right autopilot was flying the airplane and did not disengage. This made us suspect that the screen on the right FMC failed but not the unit itself. Nevertheless it made the unit unusual and since it is directly linked to the aircraft navigation system we complied with regulations and reported a partial loss of navigation capability to Iceland Center. They asked if we could still navigate satisfactory or needed to divert to which we replied that we still had satisfactory navigation capability to continue on. We then contacted Dispatch and Maintenance Control. Maintenance asked us to pull the CB to the unit and attempt a reset/registration but no change happened. Maintenance said we were safe and legal to go on to destination with the remaining FMC and all agreed. All IRU's were working perfectly and Iceland confirmed our position with a radar plot and we pressed on. Along the way we backed up our IRU data with radio bearings/LOP's/speed lines and further confirmed out course/position (yes; I do remember how to DR and do old techniques). Arrived at our oceanic exit point on target and rest of flight normal and uneventful.