The core enzyme of RNA polymerase is made up of four subunits without the sigma factor. The RNA polymerase core enzyme consists of two alpha (2α), one beta (β), one beta prime (β') and one omega (ω) subunit.

The most common example is the E.coli RNA polymerase core enzyme. Because of the absence of the sigma factor, E.coli RNA polymerase core enzyme is unable to recognize any specific bacterial or phage DNA promoters. Instead it transcribes RNA from nonspecific initiation sequences.