An incomplete particle identification distorts the observed event-by-event fluctuations of the hadron chemical composition in nucleus-nucleus collisions. A new experimental technique called the {\em identity method} was recently proposed. It eliminated the misidentification problem for one specific combination of the second moments in a system of two hadron species. In the present paper this method is extended to calculate all the second moments in a system with arbitrary number of hadron species. Special linear combinations of the second moments are introduced. These combinations are presented in terms of single-particle variables and can be found experimentally from the event-by-event averaging. The mathematical problem is then reduced to solving a system of linear equations. The effect of incomplete particle identification is fully eliminated from the final results.

11 pages