Round spiral antennas are generally designed by using Archimedean spiral geometries which have linear growth rates. To obtain smaller antennas with nearly the same performance, square spiral Archimedean geometries are also widely used instead. In this study, novel square antennas are proposed, designed and examined. At first two similar but different approaches are employed to design new antennas by considering the design procedure used to obtain log-periodic antennas. Then, the performance of these antennas is improved by considering another property of log-periodic antennas. Simulations are performed by using two different numerical methods which are Finite Difference Time Domain Method (FDTD) and Method of Moments (MoM). The results obtained from the simulations are compared with those of the Archimedean spiral antennas in terms of the frequency dependency of fundamental antenna parameters such as antenna gain and radiation pattern. The simulation results are compared with the ones obtained from the experimental study.