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This letter describes a new frequency-domain method for Maxwell's equations based on the multidomain pseudospectral method. The computational domain is first divided into nonoverlapping subdomains. Using the Chebyshev polynomials to represent the unknown field components in each subdomain, the spatial derivatives are calculated with a spectral accuracy at the Chebyshev collocation points. The physical boundary conditions at the subdomain interfaces are enforced to ensure the global accuracy. Numerical results demonstrate that the pseudospectral frequency-domain (PSFD) method has a spectral accuracy, and thus is an attractive method for large-scale problems. With only about five cells per wavelength, the results have an error less than 1% in our typical examples.