Helicopter crew departing TEB Runway 19 from the south end is cleared for takeoff and told to 'make it look like a 24 departure.' The crew misunderstood and heads 190 degrees until corrected by the Tower.

Narrative

We were awaiting release for IFR trip from TEB in the run-up block adjacent to departure end of Runway 19. We discussed the TEB5 departure instructions which said to depart runway heading to 1;500 FT; then make a right turn to heading 280 and maintain 1;500 FT until past the 4.5 DME of TEB. Tower cleared us for takeoff and told us to 'make it look like a 24 departure'. I acknowledged and read that instruction back. We took off and maintained a heading of 190 instead of 240. At approximately 1;000 FT; Tower called us and told us that we needed to be on the runway heading of 240; with which we immediately complied. We continued to 1;500 FT and made the turn to 280. Tower switched us to Departure; and I checked in at 1;500 FT; 280 heading. The Controller acknowledged; and then asked us where on the airport we had departed from. I responded and also told him that we were told to make it look like a departure from Runway 24. He then gave us climb instructions; with which we complied. At no time prior to that clearance did we go above 1;500 FT. Nothing else was said. I believe that the problem was caused by thinking that we were adjacent to the departure end of 24; instead of the departure end of 19. Next time I make a non-runway IFR departure; I will be certain that we review the area on the airport from which we are departing in addition to the instrument departure procedure. I believe that will prevent such an occurrence in the future.