SummaryA connection between a balanced fractional 2 ~ factorial design of resolution V and a balanced array of strength 4 with index set {Z0, Z~, /~2,/~3, Z~} has been established by Srivastava [3]. The purpose of this paper is to generalize his results by investigating the combinatorial property of a fraction T and the algebraic structure of the information matrix of the fractional design. Main results are: A necessary and sufficient condition for a fractional 2 ~ factorial design T of resolution 2/+1 to be balanced is that T is a balanced array of strength 2l with index set {/~0,/~1,/~,"',/~2t} provided the information matrix M is nonsingular.

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