diff --git a/cmake/Modules/FindSuiteSparse.cmake b/cmake/Modules/FindSuiteSparse.cmake
index b14105d8..ba36d608 100644
--- a/cmake/Modules/FindSuiteSparse.cmake
+++ b/cmake/Modules/FindSuiteSparse.cmake
@@ -57,14 +57,17 @@ endif (${SuiteSparse_ROOT})
 # transitive closure of dependencies; after this SuiteSparse_MODULES is the
 # full list of modules that must be found to satisfy the user's link demands
 set (SuiteSparse_MODULES ${SuiteSparse_FIND_COMPONENTS})
-list (FIND SuiteSparse_FIND_COMPONENTS "cholmod" CHOLMOD_DESIRED)
-list (FIND SuiteSparse_FIND_COMPONENTS "umfpack" UMFPACK_DESIRED)
-if (NOT CHOLMOD_DESIRED EQUAL -1)
-  list (APPEND SuiteSparse_MODULES amd camd colamd ccoilamd)
-endif (NOT CHOLMOD_DESIRED EQUAL -1)
+list (FIND SuiteSparse_MODULES "umfpack" UMFPACK_DESIRED)
 if (NOT UMFPACK_DESIRED EQUAL -1)
-  list (APPEND SuiteSparse_MODULES amd)
+  list (APPEND SuiteSparse_MODULES amd cholmod)
 endif (NOT UMFPACK_DESIRED EQUAL -1)
+list (FIND SuiteSparse_MODULES "cholmod" CHOLMOD_DESIRED)
+if (NOT CHOLMOD_DESIRED EQUAL -1)
+  list (APPEND SuiteSparse_MODULES amd camd colamd)
+endif (NOT CHOLMOD_DESIRED EQUAL -1)
+if (SuiteSparse_MODULES)
+  list (REMOVE_DUPLICATES SuiteSparse_MODULES)
+endif (SuiteSparse_MODULES)
 
 # if someone else already have found all the packages for us, then don't do anything
 set (SuiteSparse_EVERYTHING_FOUND TRUE)
@@ -114,7 +117,7 @@ if (CHOLMOD_LIBRARY)
   list (REVERSE CHOLMOD_LIBRARIES)
 endif (CHOLMOD_LIBRARY)
 if (UMFPACK_LIBRARY)
-  list (APPEND UMFPACK_LIBRARIES ${AMD_LIBRARIES})
+  list (APPEND UMFPACK_LIBRARIES ${CHOLMOD_LIBRARIES} ${AMD_LIBRARIES})
   list (REVERSE UMFPACK_LIBRARIES)
   list (REMOVE_DUPLICATES UMFPACK_LIBRARIES)
   list (REVERSE UMFPACK_LIBRARIES)