Abstract: The lambda method with Z transformation is valid and fast.It has been widely used to enhance the performance of the search arithmetic in GPS data processing problem.However, the lambda Z transformation is face to the probably of invalidation when the condition number is large.Propose a new arithmetic called test and compensated Z transformation to avoid the risk of invalidation.Though the performance of test and compensate Z transformation in processing measured data, it is clear that this new arithmetic perform well and success rate of Z transformation can be enhanced.