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We give a new proof of the derived equivalence of a pair of varieties connected by the flop of type  C  2  in the list of Kanemitsu (2018), which is originally due to Segal (Bull. Lond. Math. Soc.,  48  (3) 533–538, 2016). We also prove the derived equivalence of a pair of varieties connected by the flop of type    ${A}_{4}^{G}$  A 4 G in the same list. The latter proof follows that of the derived equivalence of Calabi–Yau 3-folds in Grassmannians Gr(2,5) and Gr(3,5) by Kapustka and Rampazzo (Commun. Num. Theor. Phys.,  13  (4) 725–761 2019) closely.

Derived Equivalences for the Flops of Type C2 and ${A}_{4}^{G}$ via Mutation of Semiorthogonal Decomposition