Abstract: A principle of inverse compensation computation and concept of perfect conservative scheme which can provide new approach for improvement of traditional schemes is set up in this paper. Especially, two direct formulation theroms of square and weighted square perfect conservative time difference scheme, which can solve their problem of nonlinear computational instability thoroughly and reasonably, is given here. This compensation principle and inverse approach is also workable in formulation of time-space discrete perfect conservative scheme and that of other characteristic properties.The time-space discrete perfect conservative schemes of(weighed) square and non-square(kinetic) energy, enstrophy and angular momentum property is further realized respectively by application of inveres compensation theory to improvement of a traditional numerical weather prediction spectral scheme of barotropicprimitiveequation.The numericalexperiments of them showthatperfectconserva-tive schemes can improve computational precision, prolong valid integral time and reduce the amount of computation greatly in comparison with the corresponding traditional scheme, and perfect conservative schemes of some "good" property can solve the problems of nonlinear computational instability and nonlinear convergence in practice.

Key words: perfect conservative scheme, inverse compensation principle, computational valid time, amount of computation, nonlinear computational instability