A burner control system with an interrupted or intermittent type of pilot burner has a special feature allowing transitions between a pilot flame hold state where the pilot flame only burns and the run state where the main burner is operating. Each transition to the pilot flame hold state from the run state comprises a brief period in which presence of the pilot flame is assured while the main flame is extinguished. Transitions to the run state from the pilot flame hold state may proceed directly through the main flame establishment period to the run state, thereby eliminating the time-consuming purging and pilot flame ignition phases.