We study the numerical solution of 3d time-harmonic Maxwell's equations by a hybridizable discontinuous Galerkin method. A hybrid term representing the tangential component of the numerical trace of the magnetic field is introduced. The global system to solve only involves the hybrid term as unknown. We show that the reduced system has properties similar to wave equation discretizations and the tangential components of the numerical traces for both electric and magnetic fields are single-valued. On the example of a plane wave propagation in vacuum the approximate solutions for both electric and magnetic fields have an optimal convergence order.