We propose a new diagram, the Kinematic-Excitation diagram (KEx diagram), which uses the [OIII]/Hbeta line ratio and the [OIII]5007 emission line width (sigma_{[OIII]}) to diagnose the ionization source and physical properties of the Active Galactic Nuclei (AGNs) and the star-forming galaxies (SFGs). The KEx diagram is a suitable tool to classify emission-line galaxies (ELGs) at intermediate redshift because it uses only the [OIII]5007 and Hbeta emission lines. We use the SDSS DR7 main galaxy sample and the Baldwin-Phillips-Terlevich (BPT) diagnostic to calibrate the diagram at low redshift. We find that the diagram can be divided into 3 regions: one occupied mainly by the pure AGNs (KEx-AGN region), one dominated by composite galaxies (KEx-composite region), and one contains mostly SFGs (KEx-SFG region). AGNs are separated from SFGs in this diagram mainly because they preferentially reside in luminous and massive galaxies and have high [OIII]/Hbeta. The separation of AGN from star-forming galaxies is even cleaner thanks to the additional 0.15/0.12 dex offset in [OIII] line width at fixed luminosity/stellar mass. We apply the KEx diagram to 7,866 galaxies at 0.3 < z < 1 in the DEEP2 Galaxy Redshift Survey, and compare it to an independent X-ray classification scheme using Chandra observation. X-ray AGNs are mostly located in the KEx-AGN region while X-ray SFGs are mostly located in the KEx-SFG region. Almost all of Type1 AGNs lie in the KEx-AGN region. These confirm the reliability of this classification diagram for emission line galaxies at intermediate redshift. At z~2, the demarcation line between star-forming galaxies and AGNs should shift 0.3 dex higher in sigma_{[OIII]} to account for evolution.
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