diff --git a/shapes/core.ttl b/shapes/core.ttl
index 5231397..75df289 100644
--- a/shapes/core.ttl
+++ b/shapes/core.ttl
@@ -676,44 +676,31 @@
     Represents a Expression Map.
     """ ;
     sh:message """
-    Expression Map requires one rml:template or one rml:constant or one
+    Expression Map may require one rml:template or one rml:constant or one
     rml:reference.
     """ ;
-    sh:property [ rdfs:label "template/constant/reference/returnMap/functionExecution" ;
+    sh:or ( [ sh:not [ sh:property [ sh:minCount 1 ;
+                                sh:path rml:returnMap ] ] ] [ sh:property [ sh:maxCount 1 ;
+                        sh:minCount 1 ;
+                        sh:path rml:returnMap ],
+                    [ sh:maxCount 1 ;
+                        sh:minCount 1 ;
+                        sh:path rml:functionExecution ] ] ) ;
+    sh:property [ rdfs:label "template/constant/reference/functionExecution" ;
             rdfs:comment """
-        Exactly one rml:template, one rml:constant, one rml:reference,
-        one rml:returnMap, or one rml:functionExecution is required.
+            Only one rml:template, one rml:constant, one rml:reference,
+            or one rml:functionExecution is allowed. rml:returnMap is only allowed if rml:functionExecution is present.
         """ ;
             sh:maxCount 1 ;
             sh:message """
         Exactly one rml:template, one rml:constant, one rml:reference,
         one rml:returnMap, or one rml:functionExecution is required.
         """ ;
-            sh:minCount 1 ;
-            sh:path [ sh:alternativePath ( rml:template rml:constant rml:reference rml:returnMap rml:functionExecution ) ] ;
+            sh:path [ sh:alternativePath ( rml:template rml:constant rml:reference rml:functionExecution ) ] ;
             sh:targetSubjectsOf rml:constant,
                 rml:functionExecution,
                 rml:reference,
-                rml:returnMap,
                 rml:template ],
-        [ rdfs:label "reference" ;
-            rdfs:comment """
-        A reference rml:reference is used to refer to a column in case of 
-        databases, a record in case of CSV or TSV data source, an element in 
-        case of XML data source, an object in case of a JSON data source, etc.
-
-        A reference must be a valid identifier, considering the reference 
-        formulation (rml:referenceFormulation) specified. The reference can be
-        an absolute path, or a path relative to the iterator specified at the 
-        logical source. 
-        """ ;
-            sh:datatype xsd:string ;
-            sh:message """
-        rml:reference must be a string.
-        """ ;
-            sh:nodeKind sh:Literal ;
-            sh:path rml:reference ;
-            sh:targetSubjectsOf rml:reference ],
         [ rdfs:label "returnMap" ;
             rdfs:comment """
         A Return Map rml:returnMap is used to define the return values of a FnO
@@ -761,7 +748,25 @@
         rml:constant must be an IRI or Literal.
         """ ;
             sh:path rml:constant ;
-            sh:targetSubjectsOf rml:constant ] .
+            sh:targetSubjectsOf rml:constant ],
+        [ rdfs:label "reference" ;
+            rdfs:comment """
+        A reference rml:reference is used to refer to a column in case of 
+        databases, a record in case of CSV or TSV data source, an element in 
+        case of XML data source, an object in case of a JSON data source, etc.
+
+        A reference must be a valid identifier, considering the reference 
+        formulation (rml:referenceFormulation) specified. The reference can be
+        an absolute path, or a path relative to the iterator specified at the 
+        logical source. 
+        """ ;
+            sh:datatype xsd:string ;
+            sh:message """
+        rml:reference must be a string.
+        """ ;
+            sh:nodeKind sh:Literal ;
+            sh:path rml:reference ;
+            sh:targetSubjectsOf rml:reference ] .
 
 <http://w3id.org/rml/shapes/RMLLogicalTargetPropertiesShape> a sh:PropertyShape ;
     rdfs:label "logicalTarget" ;
diff --git a/shapes/expression_map.ttl b/shapes/expression_map.ttl
index fc10303..35e23db 100644
--- a/shapes/expression_map.ttl
+++ b/shapes/expression_map.ttl
@@ -16,7 +16,7 @@
     Represents a Expression Map.
     """ ;
     sh:message """
-    Expression Map requires one rml:template or one rml:constant or one
+    Expression Map may require one rml:template or one rml:constant or one
     rml:reference.
     """ ;
 
@@ -26,23 +26,20 @@
         sh:targetSubjectsOf rml:template ;
         sh:targetSubjectsOf rml:constant ;
         sh:targetSubjectsOf rml:reference ;
-        sh:targetSubjectsOf rml:returnMap ;
         sh:targetSubjectsOf rml:functionExecution ;
         sh:path [sh:alternativePath (rml:template 
                                      rml:constant
                                      rml:reference
-                                     rml:returnMap
                                      rml:functionExecution)] ;
-        rdfs:label "template/constant/reference/returnMap/functionExecution" ;
+        rdfs:label "template/constant/reference/functionExecution" ;
         rdfs:comment """
-        Exactly one rml:template, one rml:constant, one rml:reference,
-        one rml:returnMap, or one rml:functionExecution is required.
+            Only one rml:template, one rml:constant, one rml:reference,
+            or one rml:functionExecution is allowed. rml:returnMap is only allowed if rml:functionExecution is present.
         """ ;
         sh:message """
         Exactly one rml:template, one rml:constant, one rml:reference,
         one rml:returnMap, or one rml:functionExecution is required.
         """ ;
-        sh:minCount 1 ;
         sh:maxCount 1 ;
     ] ;
 
@@ -134,4 +131,29 @@
         sh:nodeKind sh:BlankNodeOrIRI ;
         # Allow BlankNodes so nested structurces works as well for rml:returnMap
     ] ;
+    # If returnMap appears, then functionExecution must also appear
+    sh:or (
+
+      [
+        sh:not [
+          sh:property [
+            sh:path rml:returnMap ;
+            sh:minCount 1
+          ]
+        ]
+      ]
+
+      [
+        sh:property [
+          sh:path rml:returnMap ;
+          sh:minCount 1 ;
+          sh:maxCount 1
+        ] ;
+        sh:property [
+          sh:path rml:functionExecution ;
+          sh:minCount 1 ;
+          sh:maxCount 1
+        ]
+      ]
+    )
 .