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Eutectic and near-eutectic high entropy alloys (HEAs) have recently attracted a great deal of interest because of their promising properties, such as an excellent castability and unique combination of good ductility and high strength. However, in the absence of a phase diagram, it remains a non-trivial task to find a eutectic or near-eutectic composition for a HEA system, which usually demands a tremendous amount of efforts if a trial-and-error approach is followed. In this paper, we briefly review the thermodynamics that governs the eutectic solidification in regular binary and ternary alloys, and proceed to the discussion for the design of eutectic HEAs. Based on the data reported, we then propose an improved strategy which may enable an efficient search for the eutectic or near eutectic HEA compositions.