diff --git a/clippy_lints/src/functions.rs b/clippy_lints/src/functions.rs
index 94200a154..30814e869 100644
--- a/clippy_lints/src/functions.rs
+++ b/clippy_lints/src/functions.rs
@@ -1,7 +1,7 @@
 use crate::utils::{
     attr_by_name, attrs::is_proc_macro, is_must_use_ty, is_trait_impl_item, is_type_diagnostic_item, iter_input_pats,
-    last_path_segment, match_def_path, must_use_attr, path_to_local, return_ty, snippet, snippet_opt, span_lint,
-    span_lint_and_help, span_lint_and_then, trait_ref_of_method, type_is_unsafe_function,
+    match_def_path, must_use_attr, path_to_local, return_ty, snippet, snippet_opt, span_lint, span_lint_and_help,
+    span_lint_and_then, trait_ref_of_method, type_is_unsafe_function,
 };
 use if_chain::if_chain;
 use rustc_ast::ast::Attribute;
@@ -470,12 +470,11 @@ fn check_result_unit_err(cx: &LateContext<'_>, decl: &hir::FnDecl<'_>, item_span
     if_chain! {
         if !in_external_macro(cx.sess(), item_span);
         if let hir::FnRetTy::Return(ref ty) = decl.output;
-        if let hir::TyKind::Path(ref qpath) = ty.kind;
-        if is_type_diagnostic_item(cx, hir_ty_to_ty(cx.tcx, ty), sym::result_type);
-        if let Some(ref args) = last_path_segment(qpath).args;
-        if let [_, hir::GenericArg::Type(ref err_ty)] = args.args;
-        if let hir::TyKind::Tup(t) = err_ty.kind;
-        if t.is_empty();
+        let ty = hir_ty_to_ty(cx.tcx, ty);
+        if is_type_diagnostic_item(cx, ty, sym::result_type);
+        if let ty::Adt(_, substs) = ty.kind();
+        let err_ty = substs.type_at(1);
+        if err_ty.is_unit();
         then {
             span_lint_and_help(
                 cx,
diff --git a/tests/ui/result_unit_error.rs b/tests/ui/result_unit_error.rs
index 5e57c752b..a4ec80302 100644
--- a/tests/ui/result_unit_error.rs
+++ b/tests/ui/result_unit_error.rs
@@ -1,6 +1,4 @@
-#![allow(clippy::unnecessary_wraps)]
-#[warn(clippy::result_unit_err)]
-#[allow(unused)]
+#![warn(clippy::result_unit_err)]
 
 pub fn returns_unit_error() -> Result<u32, ()> {
     Err(())
@@ -36,4 +34,23 @@ impl UnitErrorHolder {
     }
 }
 
+// https://github.com/rust-lang/rust-clippy/issues/6546
+pub mod issue_6546 {
+    type ResInv<A, B> = Result<B, A>;
+
+    pub fn should_lint() -> ResInv<(), usize> {
+        Ok(0)
+    }
+
+    pub fn should_not_lint() -> ResInv<usize, ()> {
+        Ok(())
+    }
+
+    type MyRes<A, B> = Result<(A, B), Box<dyn std::error::Error>>;
+
+    pub fn should_not_lint2(x: i32) -> MyRes<i32, ()> {
+        Ok((x, ()))
+    }
+}
+
 fn main() {}
diff --git a/tests/ui/result_unit_error.stderr b/tests/ui/result_unit_error.stderr
index 12901b354..41d8b0a7c 100644
--- a/tests/ui/result_unit_error.stderr
+++ b/tests/ui/result_unit_error.stderr
@@ -1,5 +1,5 @@
 error: this returns a `Result<_, ()>
-  --> $DIR/result_unit_error.rs:5:1
+  --> $DIR/result_unit_error.rs:3:1
    |
 LL | pub fn returns_unit_error() -> Result<u32, ()> {
    | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
@@ -8,7 +8,7 @@ LL | pub fn returns_unit_error() -> Result<u32, ()> {
    = help: use a custom Error type instead
 
 error: this returns a `Result<_, ()>
-  --> $DIR/result_unit_error.rs:14:5
+  --> $DIR/result_unit_error.rs:12:5
    |
 LL |     fn get_that_error(&self) -> Result<bool, ()>;
    |     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
@@ -16,7 +16,7 @@ LL |     fn get_that_error(&self) -> Result<bool, ()>;
    = help: use a custom Error type instead
 
 error: this returns a `Result<_, ()>
-  --> $DIR/result_unit_error.rs:16:5
+  --> $DIR/result_unit_error.rs:14:5
    |
 LL |     fn get_this_one_too(&self) -> Result<bool, ()> {
    |     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
@@ -24,12 +24,20 @@ LL |     fn get_this_one_too(&self) -> Result<bool, ()> {
    = help: use a custom Error type instead
 
 error: this returns a `Result<_, ()>
-  --> $DIR/result_unit_error.rs:34:5
+  --> $DIR/result_unit_error.rs:32:5
    |
 LL |     pub fn unit_error(&self) -> Result<usize, ()> {
    |     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    |
    = help: use a custom Error type instead
 
-error: aborting due to 4 previous errors
+error: this returns a `Result<_, ()>
+  --> $DIR/result_unit_error.rs:41:5
+   |
+LL |     pub fn should_lint() -> ResInv<(), usize> {
+   |     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+   |
+   = help: use a custom Error type instead
+
+error: aborting due to 5 previous errors