The calculation of the coefficients of the linear best method for restoring the second derivative at zero of a bounded analytical function given in a unit circle by the values of the function and its derivative at specified points forming a regular polygon centered at zero is pointed in that paper. It also determines the error of the best method and finds the corresponding extreme function. It is proved that the extremal function is unique. At the end of the work, formulas are got that can be used to calculate the coefficients of the linear best method. In finding of these formulas, the method of duality of extreme problems was applied, which was deeply developed by S.Y. Havinson. It is proved that these coefficients are the only one.

Keywords: optimal recovery, error of the best method, linear best method, coefficients of the linear best method