This study of nitrogen-diluted non-premixed counterflow flames with finite burner diameters investigates the important role of the outer-edge flame on flame extinction through experimental and numerical analyses. It explores flame stability diagrams mapping the flame extinction response of nitrogen-diluted non-premixed counterflow flames to varying global strain rates in terms of burner diameter, burner gap, and velocity ratio. A critical nitrogen mole fraction exists beyond which the flame cannot be sustained; the critical nitrogen mole fraction versus global strain rate curves have C-shapes for various burner diameters, burner gaps, and velocity ratios. At sufficiently high strain-rate flames, these curves collapse into one curve; therefore, the flames follow the one-dimensional flame response of a typical diffusion flame. Low strain-rate flames are significantly affected by radial conductive heat loss, and therefore flame length. Three flame extinction modes are identified: flame extinction through shrinkage of the outer-edge flame with or without oscillations at the outer-edge flame prior to the extinction, and flame extinction through a flame hole at the flame center. The extinction modes are significantly affected by the behavior of the outer-edge flame. Detailed explanations are provided based on the measured flame-surface temperature and numerical evaluation of the fractional contribution of each term in the energy equation. Radial conductive heat loss at the flame edge to ambience is the main mechanism of extinction through shrinkage of the outer-edge flame in low strain-rate flames. Reduction of the burner diameter can extend the flame extinction mode by shrinking the outer-edge flame in higher strain-rate flames. © 2012 Elsevier Ltd. All rights reserved.