This paper consists of two parts. The first part gives a description of the motion of large eddies in a turbulent flow. The non-stationary character of the large eddies is emphasized. Up to present, there appears to be some confusion regarding the law of turbulence decay, especially the variation of the microscale with time. This paper introduces a new characteristic length for large eddies which leads to a new decay law valid at the initial period. The apparent discrepancies between Kolmogoroffs decay law and Lin's decay law are seen to be due to different expansions of the present one. It is hoped that the physical picture described herein would give some further insight into the structure of turbulence. In the second part, an analysis similar to that adopted iby Sedov for the correlation coefficients is applied to the turbulent spectrum. New results are obtained, in particular the transition of the decay law from the initial period to the final period.