A turbulent premixed flame is decomposed into the three layers of internal region of fluctuating flamelets and leading and trailing edges with negligible density variation in the nonflamelet regime. Conditional averaging is performed in terms of the successively higher order differentials of c, (1 - c), Sigma(f)' (= -partial derivative c/partial derivative n) and partial derivative(2)c/partial derivative n(2) to derive conditional relationships through the layered brush structure. The leading edge is defined as the region of negligible mean reaction rate to avoid the cold boundary difficulty for existence of a steadily propagating flame. The leading and trailing edges are identified in terms of the length scales of exponential decay, L-LE and L-TE, for (c) over bar and (1 - (c) over bar) becoming equal to that for Sigma(f), as (c) over bar approaches zero and unity respectively. Analytical expressions are derived for L-LE and L-TE which are in good agreement with DNS results except for L-TE interacting with the wall boundary layer in the stagnating flame. The turbulent burning velocity, S-T, is given by the total diffusivity, (D-m + D-t), divided by L-LE with its two limiting forms at strong and weak turbulence. The new (c) over bar transport equation is given in terms of the turbulent diffusivity, D-ts, which is defined for the flux, < V'(Sigma(f)')'>, free from countergradient diffusion due to volume expansion. A rigorous expression is derived for the derivative, d Sigma(f)/d (c) over bar, in terms of the mean orientation vectors and curvature, < n >(f), < n >(K) and (f). It is consistent with a familiar parabolic profile of Sigma(f) for approximately uniform < n >(f) and (f) in the (c) over bar space. The conditional velocities show the asymptotic behavior of < v >(u) approaching < v > and < v >(b) approaching < v >(f) at the leading edge and < v >(b) approaching < v > and < v >(u) approaching < v >(f) at the trailing edge. Good agreement is shown for the analytical expressions of S-T and the integrated profiles of Sigma(f) with DNS results of the two test flames in statistical steadiness. (C) 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.