(*steve*), the data sheet says that the D-suffix version of the L293 has the protection diodes built in.
I think you have the sequence wrong. If your sequence numbers on the four control signals are right, you will have the following sequence of signals on the stepper motor windings:
1. Gap, then winding L1 energised, positive to left end
2. Gap, then winding L1 energised, negative to left end
3. Gap, then winding L2 energised, positive to left end
4. Gap, then winding L2 energised, negative to left end.
I'm not sure how your stepper motor is designed, but I think the correct sequence should be:
1. Gap, then winding L1 energised, positive to left end
2. Gap, then winding L2 energised, positive to left end
3. Gap, then winding L1 energised, negative to left end
4. Gap, then winding L2 energised, negative to left end.
As I say, I'm not sure about this. Perhaps you could divulge a bit more of your secret information and tell us the part number of the stepper motor, and perhaps a reference to its data sheet.
Edit: Aha, (*steve*) has already pointed you to the answer to the correct order of control signals, on the Ben's HobbyCorner site.