We present high resolution echelle spectra taken during four observing runs from 1999 to 2001 of the recently X-ray/EUV selected chromospherically active binary BK Psc (2RE J0039+103). Our observations confirm the single-lined spectroscopic binary(SB1) nature of this system and allow us to obtain, for the first time,the orbital solution of the system as in the case of a SB2 system. We have determined precise radial velocities of both components: for the primary by using the cross correlation technique, and for the secondary by using its chromospheric emission lines. We have obtained a circular orbit with an orbital period of 2.1663 days, very close to its photometric period of 2.24 days (indicating synchronous rotation). The spectral type (K5V) we determined for our spectra and the mass ratio (1.8) and minimum masses (Msin^{3}i) resulting from the orbital solution are compatible with the observed K5V primary and an unseen M3V secondary. Using this spectral classification, the projected rotational velocity (vsini, of 17.1 km/s}) obtained from the width of the cross-correlation function and the data provided by Hipparcos, we have derived other fundamental stellar parameters. The kinematics and the non-detection of the LiI line indicate that it is an old star. The analysis of the optical chromospheric activity indicators from the CaII H & K to CaII IRT lines, by using the spectral subtraction technique, indicates that both components of the binary system show high levels of chromospheric activity. H_alpha emission above the continuum from both components is a persistent feature of this system during the period 1999 to 2001 of our observations as well as in previous observations.
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