Based on the relationship between cheating immune secret sharing and cryptogTaphic criteria of Boolean functions, to design a cheating immune secret sharing scheme, a 1-resilient function satisfy- ing the strict avalanche criterion (SAC) is needed. In this paper, a technique on constructing a cheating immune secret sharing function is studied. By using Maiorana-McFarland construction tech- nique, two new methods to construct cheating immune secret sharing functions are proposed.