The shapes occurring in the images are important in the content-based image retrieval. In this paper we introduce a new Fourier-based descriptor for the characterization of the shapes for retrieval purposes. This descriptor combines the benefits of the wavelet transform and Fourier transform. This way the Fourier descriptors can be presented in multiple scales, which improves the shape retrieval accuracy of the commonly used Fourier-descriptors. The multiscale Fourier descriptor is formed by applying the complex wavelet transform to the boundary function of an object extracted from an image. After that, the Fourier transform is applied to the wavelet coefficients in multiple scales. This way the multiscale shape representation can be expressed in a rotation invariant form. The retrieval efficiency of this multiscale Fourier descriptor is compared to an ordinary Fourier descriptor and CSS-shape representation.