For better control of a lean premixed combustion system, it is necessary to understand the mechanism of unsteady cellular flame. The objective of the present study is to investigate how heat loss influences the cellular instability of lean premixed flame. The lean premixed CH4/H-2/air cellular flames generated on a McKenna burner were studied, and heat loss was responsible for the manifestation of unsteady cellular structure. A method of applying proper orthogonal decomposition in scale analysis is presented, which has proven helpful in characterizing the cellular flame. The multiple scale nature of unstable cellular flame was identified, and the small scales were found to act in the random movement of cells. The contribution of each scale is obtained. The energy distribution on modes indicates that the energy on higher-order modes, equivalently the contribution of smaller scales, is decreased with decreasing heat loss. Through analyzing the principal modes and temporal coefficients, heat loss is found to influence a flame's unstable behavior by promoting the oscillation of large scales, and the wrinkling factor is estimated. It is found that there is a cut-off length scale, below which the wrinkles make little contribution to the enhancement of combustion intensity.