Abstract: In this paper, it is pointed out that in most of the previous works about the stability of coronal magnetic loops, a rigid boundary condition is used (although sometimes without being mentioned) at the edge of a loop, which has a great influence on the result too large to be ignored, even if the pressure gradient is favourable. On the other hand, corona conditions are quite different from that in laboratories. Is it proper to use the rigid boundary condition at the edge of a loop? And what is the mechanism that makes the condition realized? They are still the questions open to further discussions.Besides, if m=1 is stable, according to Newcomb's theorem, it is unnecessary to consider the modes of m> 1; but if it is not stable, it will not be enough to examine m= 1 only. And this article shows that, sometimes, the modes of m > 1 may be more instable.Instead of using a marginal stability analysis such as many authors did, the MHD momentum equation of compressible fluid is used in this paper, so that both the instability region and the growth rate of instability can be obtained at the same time. In addition. the difficulties associated with the singularity in marginal stability analysis could then be avoided.