Taylor Couette flow is characterized by its spatial periodicity, often treated in various types of symmetry. They are treated as shift symmetry and shift-reflect symmetry in a landmark numerical simulation by Markus and Coughlin , and so-called periodic boundary condition is used in most of numerical works such as the DNS calculation by Ostilla . By experimental observation of flow field in the whole column area, Vr(r,z), such symmetries are shown to be valid in small range of R* (reduced Re number), but a reflect symmetry is easily broken. This is shown in quantitative way of velocity profile for the whole length of axis at mid-gap location and it is verified only for TVF, but not for WVF. In considering such symmetry breaking scenario, one old experimental observation of appearance of multiplet structure of power spectrum indicates an invalidity of periodical boundary condition, which is commonly used in numerical work.