Semi-supervised　learning　(SSL)　employs　unlabeled　data　with　limited　labeled　samples　to　enhance　deep　networks,　but　imbalance　degrades　performance　due　to　biased　pseudo-labels　skewing　decision　boundaries.　To　address　this　challenge,　we　propose　two　optimization　conditions　inspired　by　our　theoretical　analysis.　These　conditions　focus　on　aligning　class　distributions　and　representations.　Additionally,　we　introduce　a　plug-and-play　method　called　Basis　Transformation　based　distribution　alignment　(BTDA)　that　efficiently　aligns　class　distributions　while　considering　inter-class　relationships.　BTDA　mitigates　the　negative　impact　of　biased　pseudo-labels　through　basis　transformation,　which　involves　a　learnable　transition　matrix.　Extensive　experiments　demonstrate　the　effectiveness　of　integrating　existing　SSL　methods　with　BTDA　in　image　classification　tasks　with　class　imbalance.　For　example,　BTDA　achieves　accuracy　improvements　ranging　from　2.47　to　6.66%　on　CIFAR10-LT　and　SVHN-LT　datasets,　and　a　remarkable　10.95%　improvement　on　the　tail　class,　even　under　high　imbalanced　rates.　Despite　its　simplicity,　BTDA　achieves　state-of-the-art　performance　in　SSL　with　class　imbalance　on　representative　datasets.　©　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature　2024.