An Al—Mn—Cr—Si alloy, rapidly solidified by means of melt-spinning in a moderate vacuum, has been studied by transmission electron microscopy. The material is found to consist of fine icosahedral quasicrystalline precipitates in an aluminium matrix. Electron diffraction patterns and high-resolution electron microscopy show a high degree of coherence between the quasicrystals and the matrix giving a strict orientational relationship. Coherence strain between the particles and the matrix is found on both sides of the interface. In the quasicrystal the strain is seen to distort the structure, changing it locally. This is verified by Fourier transforms of the observed images. The transforms can also explain the changes in period and in direction of moiré fringes found between the matrix and the precipitates. On the aluminium side of the interface a periodic strain is observed. This period may be ascribed to the small difference between the Al (200) planes and the (110000) quasi-lattice planes spacings.