In this Letter, highly resolved measurements of the horizontal velocity inside the boundary layer of turbulent Rayleigh-Bénard convection are reported. They were performed in a cylindrical box with an aspect ratio Gamma=1.13 which was filled with air with a Prandtl number Pr=0.7. The horizontal velocity was measured along the central axis close to the cooling plate in a range of Rayleigh numbers between Ra=10;{11} and Ra=10;{12} using a two-dimensional laser Doppler velocimeter. We demonstrate that the profile of the mean velocity strongly differs from that of classical shear flows like the Blasius shape of a laminar flat plate boundary layer or a turbulent logarithmic velocity profile with standard coefficients.