The magnetoimpedance (MI) of a glass-coated amorphous ${\mathrm{Co}}_{83.2}{\mathrm{Mn}}_{7.6}{\mathrm{Si}}_{5.8}{\mathrm{B}}_{3.3}$ microwire has been studied up to a frequency of 11 MHz and varying a dc magnetic field ${(H}_{\mathrm{dc}})$ within \ifmmode\pm\else\textpm\fi{}140 Oe. Giant magnetoimpedance (GMI) effect has been observed within a frequency range, $f\ensuremath{\sim}1\char21{}8\mathrm{MHz}$ with a maximum change of 53% around 4 MHz. At low frequency $(fl6\mathrm{MHz}),$ maximum value of MI is observed at ${H}_{\mathrm{dc}}=0$ when measured against ${H}_{\mathrm{dc}}$ whereas high frequency $(fg6\mathrm{MHz})$ results show the appearance of two peaks at nonzero values of ${H}_{\mathrm{dc}}.$ The effect of axial tensile stress (maximum 566 MPa) and current amplitude (0.2\char21{}5.0 mA) on MI has been studied. The application of external stress changes the MI results to a large extent whereas almost no change in MI is observed due to the change in current amplitude. The magnetization of the same sample has also been measured in presence of different tensile stresses to understand the domain structure and magnetoimpedance results. The experimental results of GMI have been explained considering the skin effect in the frequency range of MHz. The applied dc magnetic field changes the circular permeability and the penetration depth of the ac current which in turn changes the impedance of the sample.