Transmission spectra of near-self-complementary metallic checkerboard patterns (MCPs) exhibit a drastic change when the metal squares are brought into contact with each other from a noncontact state. Transmission spectra of near-self-complementary samples, which are fabricated by printing technology, show rather gradual systematic change with changing the nominal metal square size while keeping the period because of randomness naturally introduced by the limited accuracy of the printer. The spectra have transmission-invariant frequencies, which means that the spectra are a superposition of two types of spectra, the ratio of which depends on the nominal square size. The correlation seen in the real and imaginary parts of the complex amplitude spectra can be interpreted based on the Kramers-Kronig relation. As an application of the sensitiveness of the transmission spectrum of the MCPs to connectivity of the metal squares, the revealing of an optically hidden pattern by a terahertz beam is demonstrated.