Exact solution of transient dynamics for sequential associative memory model is derived through the path-integral method. The path-integral method can provide exact solutions of models. However only stationary states have been discussed. In order to analyze transient dynamics, we analyze the correlation of crosstalk noise and derive the exact solution of transient dynamics. Surprisingly the exact solution is equivalent to result derived through the statistical neurodynamics, which assumes that the crosstalk noise is normally distributed. In order to examine the theoretical finding, we numerically obtained cumulants of the crosstalk noise. We verify that the 3rd and 4th-order cumulants are equal to zero, and the crosstalk noise is normally distributed even in the non-retrieval case. Moreover, we show that results obtained by the theory agree with those obtained by the simulations, and found that the macroscopic unstable state completely coincides with the separatrix.