Fano resonances are observed in a composite metamaterial that consists of an electric split ring resonator eSRR and an I-shaped resonator ISR. By adjusting the length of the ISR the degree of asymmetry in the line shape of the composite metamaterial can be controlled and even made to be symmetric. In contrast to other methods to create Fano resonances, the individual modes of the eSRR and ISR have the same symmetry and are not evanescently coupled to each other. The transmission is simulated using the finite difference time domain method and a coupled oscillator model is used to obtain nominal values of the Fano asymmetry factor q. Composite metamaterials and individual eSRR and ISR metamaterials are fabricated, and their transmission is measured with terahertz time-domain spectroscopy.