diff --git a/cmake/thirdParties.cmake b/cmake/thirdParties.cmake
index 4d0b4846..41ae83db 100644
--- a/cmake/thirdParties.cmake
+++ b/cmake/thirdParties.cmake
@@ -60,9 +60,12 @@ if(HDF5_FOUND)
     elseif(TARGET hdf5)
         # target from hdf5 1.8 config
         target_link_libraries(MATIO::HDF5 INTERFACE hdf5)
-    elseif(TARGET HDF5::HDF5)
+    elseif(TARGET hdf5::hdf5-shared)
         # target defined in CMake FindHDF5 (since 3.19)
-        target_link_libraries(MATIO::HDF5 INTERFACE HDF5::HDF5)
+        target_link_libraries(MATIO::HDF5 INTERFACE hdf5::hdf5-shared)
+    elseif(TARGET hdf5::hdf5-static)
+        # target defined in CMake FindHDF5 (since 3.19)
+        target_link_libraries(MATIO::HDF5 INTERFACE hdf5-static)
     else()
         # results from CMake FindHDF5
         set_target_properties(MATIO::HDF5 PROPERTIES