It has been reported that the MDCK cell tight junction shows stochastic fluctuation and forms the interdigitation structure, but the mechanism of the pattern formation remains to be elucidated. In the present study, we first quantified the shape of the cell-cell boundary at the initial phase of pattern formation. We found that the Fourier transform of the boundary shape shows linearity in the log-log plot, indicating the existence of scaling. Next, we tested several working hypotheses and found that the Edwards-Wilkinson equation, which consists of stochastic movement and boundary shortening, can reproduce the scaling property. Next, we examined the molecular nature of stochastic movement and found that myosin light chain puncta may be responsible. Quantification of boundary shortening indicates that mechanical property change may also play some role. Physiological meaning and scaling properties of the cell-cell boundary are discussed.