Summary: Let \(\widetilde{A}=A+E\) be a perturbed matrix of the matrix \(A\). The estimation about the Euclid distance between the spectrums of matrices \(\widetilde{A}\) and \(A\) has been studied extensively. In this paper, for an arbitrary matrix \(A\), the estimates of the Euclid distance between the corresponding spectra are obtained by utilizing the idea of J. X. Chen and W. Li [Chin. J. Eng. Math., Xi’an 22, No. 1, 183–186 (2005; Zbl 1099.15503)]. The existing results are generalized.