This article examines the structure near a cold wall of the flame-tip region of a triple or tribrachial flame. A transformation of coordinates is employed that enables the energy equation to be integrated across the premixed flame (PF) are, subject to an upstream matching condition. An approximate matching condition is derived that enables a differential equation to be derived for the PF are shape. The solution of this equation produces flame contours X(Z) which may be grafted onto an orthogonal chi-Z grid as the function chi = X(Z). Comparison between the calculated and numerically computed flame shapes is favorable.