A selective 180\ifmmode^\circ\else\textdegree\fi{} pulse in the z direction is shown to refocus the second-order broadening of the (1/2)-(1/2) central transition in the spin-(5/2) nucleus $^{27}\mathrm{Al}$. Evidence for this refocusing is the formation of an echo after transverse magnetization is created by a selective 90\ifmmode^\circ\else\textdegree\fi{} x pulse, and the ${p}_{z}$ pulse following the initial decay leads to a rise and decay of magnetization. Implications for high-resolution NMR of weak quadrupolar nuclei in solids are discussed.