Although the optical colour-magnitude diagram of galaxies allows one to select red sequence objects, neither can it be used for galaxy classification without additional observational data such as spectra or high-resolution images, nor to identify blue galaxies at unknown redshifts. We show that adding the near ultraviolet colour to the optical CMD reveals a tight relation in the three-dimensional colour-colour-magnitude space smoothly continuing from the blue cloud to the red sequence. We found that 98 per cent of 225,000 low-redshift (Z<0.27) galaxies follow a smooth surface g-r=F(M,NUV-r) with a standard deviation of 0.03-0.07 mag making it the tightest known galaxy photometric relation. There is a strong correlation between morphological types and integrated NUV-r colours. Rare galaxy classes such as E+A or tidally stripped systems become outliers that occupy distinct regions in the 3D parameter space. Using stellar population models for galaxies with different SFHs, we show that (a) the (NUV-r, g-r) distribution is formed by objects having constant and exponentially declining SFR with different characteristic timescales; (b) colour evolution for exponentially declining models goes along the relation suggesting its weak evolution up-to a redshift of 0.9; (c) galaxies with truncated SFHs have very short transition phase offset from the relation thus explaining the rareness of E+A galaxies. This relation can be used as a powerful galaxy classification tool when morphology remains unresolved. Its mathematical consequence is the photometric redshift estimates from 3 broad-band photometric points. This approach works better than most existing photometric redshift techniques applied to multi-colour datasets. Therefore, the relation can be used as an efficient selection technique for galaxies at intermediate redshifts (0.3<Z<0.8) using optical imaging surveys.
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