Manifold　learning　is　an　important　class　of　methods　for　nonlinear　dimensionality　reduction.　Among　them,　the　LLE　optimisation　goal　is　to　maintain　the　relationship　between　local　neighbourhoods　in　the　original　embedding　manifold　to　reduce　dimensionality,　and　NPE　is　a　linear　approximation　to　LLE.　However,　these　two　algorithms　only　consider　maintaining　the　neighbour　relationship　of　samples　in　low-dimensional　space　and　ignore　the　global　features　between　non-neighbour　samples,　such　as　the　face　shooting　angle.　Therefore,　in　order　to　simultaneously　consider　the　nearest　neighbour　structure　and　global　features　of　samples　in　nonlinear　dimensionality　reduction,　it　can　be　linearly　calculated.　This　work　provides　a　novel　linear　dimensionality　reduction　approach　named　non-neighbour　and　neighbour　preserving　embedding　(NNNPE).　First,　we　rewrite　the　objective　function　of　the　algorithm　LLE　based　on　the　principle　of　our　novel　algorithm.　Second,　we　introduce　the　linear　mapping　to　the　objective　function.　Finally,　the　mapping　matrix　is　calculated　by　the　method　of　the　fast　learning　Mahalanobis　metric.　The　experimental　results　show　that　the　method　proposed　in　this　paper　is　effective.　©　2022　The　Author(s).　Published　by　Informa　UK　Limited,　trading　as　Taylor　&　Francis　Group.