diff --git a/src/host/linalg.jl b/src/host/linalg.jl
index 7548b4f1..79384a7d 100644
--- a/src/host/linalg.jl
+++ b/src/host/linalg.jl
@@ -111,8 +111,12 @@ if isdefined(LinearAlgebra, :copytrito!)
         LinearAlgebra.BLAS.chkuplo(uplo)
         m,n = size(A)
         m1,n1 = size(B)
-        (m1 < m || n1 < n) && throw(DimensionMismatch("B of size ($m1,$n1) should have at least the same number of rows and columns than A of size ($m,$n)"))
         if uplo == 'U'
+            if n < m
+                (m1 < n || n1 < n) && throw(DimensionMismatch("B of size ($m1,$n1) should have at least size ($n,$n)"))
+            else
+                (m1 < m || n1 < n) && throw(DimensionMismatch("B of size ($m1,$n1) should have at least size ($m,$n)"))
+            end
             @kernel function U_kernel!(_A, _B)
                 I = @index(Global, Cartesian)
                 i, j = Tuple(I)
@@ -122,6 +126,11 @@ if isdefined(LinearAlgebra, :copytrito!)
             end
             U_kernel!(get_backend(B))(A, B; ndrange = size(A))
         else  # uplo == 'L'
+            if m < n
+                (m1 < m || n1 < m) && throw(DimensionMismatch("B of size ($m1,$n1) should have at least size ($m,$m)"))
+            else
+                (m1 < m || n1 < n) && throw(DimensionMismatch("B of size ($m1,$n1) should have at least size ($m,$n)"))
+            end
             @kernel function L_kernel!(_A, _B)
                 I = @index(Global, Cartesian)
                 i, j = Tuple(I)
diff --git a/test/testsuite/linalg.jl b/test/testsuite/linalg.jl
index 7c03e69f..8de31854 100644
--- a/test/testsuite/linalg.jl
+++ b/test/testsuite/linalg.jl
@@ -85,6 +85,13 @@
                     B = zeros(T,n,n)
                     @test compare(copytrito!, AT, B, A, uplo)
                 end
+                @testset for T in eltypes, uplo in ('L', 'U')
+                    n = 16
+                    m = 32
+                    A = uplo == 'U' ? rand(T,m,n) : rand(T,n,m)
+                    B = zeros(T,n,n)
+                    @test compare(copytrito!, AT, B, A, uplo)
+                end
             end
         end