In order to search stable intermetallic compounds in a broad composition area in ternary, quaternary and higher-order systems, it is effective to utilize the calculation of formation enthalpy for screening prior to the experimental study. As the number of candidates is tremendously large for ternary and quaternary alloys, an augmented-spherical-wave (ASW) method was employed for fast calculation. To evaluate the accuracy of the calculation, the formation enthalpy of B2, L10 and B19 structures of 99 equi-atomic compounds are estimated, and the most stable structure for each alloy is compared with the literature. It is found that 75% of the reported structures are predicted by the calculation results, and B19 structure tends to be evaluated less stable than L10 structure. The formation enthalpy of Heusler-like structure with Co-Fe-Ti-Zr equi-atomic quaternary composition is also estimated and this quaternary compound is unstable comparing with the estimated formation enthalpy of binary B2-CoFe, CoZr, FeTi and FeZr. An experimental study revealed there is a phase near the composition of the quaternary compound, but the structure is Laves-C14 Fe2Zr, neither the Heusler type nor bcc-based structure. It is concluded that the combination of ASW calculation and the experimental study is suitable for a broad search of compounds with relatively symmetric structure.