Semi-supervised　learning　(SSL)　is　a　successful　paradigm　that　can　use　unlabelled　data　to　alleviate　the　labelling　cost　problem　in　supervised　learning.　However,　the　excellent　performance　brought　by　SSL　does　not　transfer　well　to　the　task　of　class　imbalance.　The　reason　is　that　the　class　bias　of　pseudo-labelling　further　misleads　the　decision　boundary.　To　solve　this　problem,　we　propose　a　new　plug-and-play　approach　to　handle　the　class　imbalance　problem　based　on　a　theoretical　extension　and　analysis　of　distribution　alignment.　The　method,　called　Basis　Transformation　Based　Distribution　Alignment　(BTDA),　efficiently　aligns　class　distributions　while　taking　into　account　inter-class　relationships.BTDA　implements　the　basis　transformation　through　a　learnable　transfer　matrix,　thereby　reducing　the　performance　loss　caused　by　pseudo-labelling　biases.　Extensive　experiments　show　that　our　proposed　BTDA　approach　can　significantly　improve　performance　in　class　imbalance　tasks　in　terms　of　both　accuracy　and　recall　metrics　when　integrated　with　advanced　SSL　algorithms.　Although　the　idea　of　BTDA　is　not　complex,　it　can　show　advanced　performance　on　datasets　such　as　CIFAR　and　SVHN.　©　The　Author(s),　under　exclusive　license　to　Springer　Nature　Singapore　Pte　Ltd.　2024.