JOHANNESBURG (Reuters) - South Africa's rand firmed against the dollar early on Wednesday as investors' confidence in the greenback was undermined by the sudden dismissal of U.S. Secretary of State Rex Tillerson. At 0640 GMT, the rand traded at 11.7750 per dollar, 0.3 percent firmer than its overnight close. U.S. President Donald Trump fired Tillerson on Tuesday after a series of rifts over policy on North Korea, Russia and Iran, replacing his chief diplomat with loyalist CIA Director Mike Pompeo. Stocks were set to open lower at 0700 GMT, with the JSE securities exchange's Top-40 futures index down 0.79 percent. In fixed income, the yield for the benchmark government bond due in 2026 fell 1 basis point to 8.085 percent. (Reporting by Olivia Kumwenda-Mtambo; Editing by Subhranshu Sahu)