Babinskaiidae is an extinct lacewing family of the superfamily Myrmeleontoidea. Hitherto, nine species of seven genera are described from the Lower and mid-Cretaceous. Here a new species of Babinskaiidae is described from Cretaceous Burmese amber, namely Parababinskaia makarkini sp. n. The new species possesses an A2 vein in the hind wing, suggesting that the loss of this vein might not be an autapomorphy of Babinskaiidae. The female of Electrobabinskaia burmana Lu, Zhang & Liu, 2017 is also described for the first time based on two specimens with their abdomens perfectly preserved, exhibiting a specialised sternum VI with paired elongate projections. A brief discussion of female genital characters is provided, which may increase our understanding of the morphology and phylogenetic position of Babinskaiidae.