A new method of estimating fluid flows near the core-mantle boundary is presented. Both the geomagnetic diffusion and dynamics in a boundary layer are taken into account under the no-slip condition at the core-mantle boundary. Below the boundary layer, the tangentially geostrophic constraint is imposed on the flow to be estimated. The radial component of the geomagnetic field just within the core is calculated from the radial component and its partial derivatives with respect to the radius, firstly, derived from continuity of the solenoidal field across the finite jump in electrical conductivity and, secondly, the geomagnetic diffusion. Below the boundary layer, fluid motions thus derived show some features common to those estimated on the basis of the frozen-flux approximation, and their accompanying vortices at mid and high latitudes are well correlated with upwellings or downwellings inside the boundary layer. The positional relation of upwellings and downwellings in equatorial regions inside and below the boundary layer suggests existence of columnar convective cells there. Intense magnetic flux spots seen in equatorial regions are likely to be produced not by downwellings at tops of cyclonic columns but by flux expulsion due to upwellings between adjacent columnar flows. The present new method leads to a new insight on core surface flows that have not been noticed so far.