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Many molecular-targeted oncology drugs have been successfully developed. The mechanism to target some specific molecules gives us the expectation that the molecular-target drug is effective over multiple tumor types and histologies. Then, simultaneous evaluation of multiple subtypes is motivated, and the basket trials aim to realize it, in which each subtype is called a basket. Although the single-arm design with simple exact binomial inference is routinely used for Phase 2 trials in standard oncology drug development, almost all recent proposals of statistical methods for basket trials are Bayesian methods of complexity. To fill the gap, the one-sample Mantel-Haenszel procedure was developed, which consists of the exact test of the global null hypothesis, the Mantel-Haenszel-type estimation of the treatment effect, and identification of effective baskets via the generalized information criterion (GIC). This paper points out an undesirable feature of the GIC in the previous research and develops an alternative one. The new GIC is free of the undesirable feature and more efficiently borrows information across baskets, which is a relevant feature for basket trials. Through numerical studies, we demonstrate that the new GIC outperforms the original one.