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A novel solution of the free convection boundary problem is represented in analytical form for velocity and temperature for an isothermal vertical plate, as an example. These fields are built as a Taylor Series in the x coordinate with coefficients as functions of the vertical coordinate (y). We restrict ourselves by cubic approximation for both functions. The basic Navier-Stokes and Fourier-Kirchhoff equations and boundary conditions give links between coefficients and connected with free convection heat transfer phenomenon which define the analytical form of the solution as a function of the Grashof number only. In the solution the non zero velocity of a fluid flow through a leading edge of the plate is taken into account. The solution in the form of velocity and temperature profiles is numerically evaluated and illustrated for air.