It is well known that an nth-order real polynomial D(z)= is Schur stable if its coefficients satisfy the monotonic condition, i.e., dn > dn-1 > > d1 > d0 > 0. In this letter it is shown that even if the monotonic condition is violated by one coefficient (say dk), D(z) is still Schur stable if the deviation of dk from dk+1 or dk-1 is not too large. More precisely we derive upper bounds for the admissible deviations of dk from dk+1 or dk-1 to ensure the Schur stability of D(z). It is also shown that the results obtained in this letter always yield the larger stability range for dk than an existing result.