Abstract: It introduces the concept of error matrix and studies the optimization model for error-eliminating program—ming．The system resource constraint is expressed by error matrix equation，and the conditions and artificial con·straints are expressed by object sets in the optimization model．All of the error matrix equations are classfied into twogroups，which are type one：AX=B，A●X=B，AAX=B，AVX=B，AAX=B；and type two：XA=B，XQA=曰，X▲A=B，XVA=B，XAA=B．The solution method，the existence of solution．and the form of solution for error—eliminating programming，based on the first kind of type two equation XA=B．have been presented．Finally，anexample of solving the problem with error—eliminating programming is given．

Key words: error—eliminating programming；system optimization；error matrix；set equation