In pursuance of the unused spectrum in higher frequencies, millimeter wave (mmWave) bands have a pivotal role. However, the high path-loss and poor scattering associated with mmWave communications highlight the necessity of employing effective beamforming techniques. In order to efficiently search for the beam to serve a user and to jointly serve multiple users it is often required to use a composite beam which consists of multiple disjoint lobes. A composite beam covers multiple desired angular coverage intervals (ACIs) and ideally has maximum and uniform gain (smoothness) within each desired ACI, negligible gain (leakage) outside the desired ACIs, and sharp edges. We propose an algorithm for designing such ideal composite codebook by providing an analytical closed-form solution with low computational complexity. There is a fundamental trade-off between the gain, leakage and smoothness of the beams. Our design allows to achieve different values in such trade-off based on changing the design parameters. We highlight the shortcomings of the uniform linear arrays (ULAs) in building arbitrary composite beams. Consequently, we use a recently introduced twin-ULA (TULA) antenna structure to effectively resolve these inefficiencies. Numerical results are used to validate the theoretical findings.