We present here a statistical study to determine the Lagrangian structure function in the anisotropic and inhomogeneous wake behind a smooth cylinder. Based on the extension of the stationary Lagrangian diffusion theory to self-similar flows, we stationarise velocity components in order to obtain Lagrangian statistics. Viggiano et al. (2011) 1 have shown how to obtain fundamental Lagrangian statistics from the anisotropic and inhomogeneous dynamics of a jet flow by normalizing the trajectories based on local Eulerian scales. In particular, computing the Lagrangian structurefunction scaling constant C0 is a crucial parameter in modelling turbulent transport. A similar role is played by the C0 constant in the Lagrangian framework as a Kolmogorov constant in the Eulerian framework. We performed direct numerical simulations (DNS) and time-resolved particle tracking velocimetry (4D-PTV) experimental analyses in the wake behind a smooth cylinder for Reynolds numbers between 300 to 3900. Details of the tracking algorithm used in the present study are addressed in Khojasteh et al. (2021) 2. Preliminary results of the experiments indicated reasonable agreement between the stationarised Lagrangian trajectories of the wake flow and the hypothesis of Lagrangian self-similarity at inertial scales.