  We study the masses of open charm and bottom tetraquark states within the
diquark-antidiquark scenario in the relativized quark model proposed by Godfrey
and Isgur. The diquark and antidiquark masses are firstly solved by relativized
quark potential, and then treated as the usual antiquark and quark,
respectively. The masses of tetraquark states are obtained by solving the
Schr\"{o}dinger-type equation between the new diquark and antidiquark. We find
the masses of $sq\bar b\bar q$ tetraquark configuration are much higher than
that of $X(5568)$. This conclusion disfavors the possibility of $X(5568)$ as a
tetraquark state within the diquark-antidiquark scenario. Further experimental
searches are needed to clarify the nature of the signal observed by D0
collaboration.
