diff --git a/Project.toml b/Project.toml
index ed3f011..2986670 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "ConstructionBase"
 uuid = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
 authors = ["Takafumi Arakaki", "Rafael Schouten", "Jan Weidner"]
-version = "1.5.3"
+version = "1.5.4"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
diff --git a/src/nonstandard.jl b/src/nonstandard.jl
index 2ba642d..4b114a7 100644
--- a/src/nonstandard.jl
+++ b/src/nonstandard.jl
@@ -56,3 +56,21 @@ constructorof(::Type{<:LinRange}) = linrange_constructor
 ### Expr: args get splatted
 # ::Expr annotation is to make it type-stable on Julia 1.3-
 constructorof(::Type{<:Expr}) = (head, args) -> Expr(head, args...)::Expr
+
+### Cholesky
+setproperties(C::LinearAlgebra.Cholesky, patch::NamedTuple{()}) = C
+function setproperties(C::LinearAlgebra.Cholesky, patch::NamedTuple{(:L,),<:Tuple{<:LinearAlgebra.LowerTriangular}})
+    return LinearAlgebra.Cholesky(C.uplo === 'U' ? copy(patch.L.data') : patch.L.data, C.uplo, C.info)
+end
+function setproperties(C::LinearAlgebra.Cholesky, patch::NamedTuple{(:U,),<:Tuple{<:LinearAlgebra.UpperTriangular}})
+    return LinearAlgebra.Cholesky(C.uplo === 'L' ? copy(patch.U.data') : patch.U.data, C.uplo, C.info)
+end
+function setproperties(
+    C::LinearAlgebra.Cholesky,
+    patch::NamedTuple{(:UL,),<:Tuple{<:Union{LinearAlgebra.LowerTriangular,LinearAlgebra.UpperTriangular}}}
+)
+    return LinearAlgebra.Cholesky(patch.UL.data, C.uplo, C.info)
+end
+function setproperties(C::LinearAlgebra.Cholesky, patch::NamedTuple)
+    throw(ArgumentError("Invalid patch for `Cholesky`: $(patch)"))
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index c31ae24..7cee50d 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -194,6 +194,52 @@ end
         @inferred constructorof(typeof(lr1))(getfields(lr2)...)
     end
 
+    @testset "Cholesky" begin
+        x = randn(3, 3)
+        X = x * x'
+        @testset "uplo=$uplo" for uplo in ['L', 'U']
+            C = Cholesky(X, uplo, 0)
+
+            # Empty patch.
+            C_new = ConstructionBase.setproperties(C, NamedTuple())
+            @test typeof(C_new) === typeof(C)
+            for f in propertynames(C)
+                @test getproperty(C_new, f) == getproperty(C, f)
+            end
+
+            # Update `L`.
+            C_new = ConstructionBase.setproperties(C, (L=2 * C.L,))
+            @test typeof(C_new) === typeof(C)
+            for f in propertynames(C)
+                @test getproperty(C_new, f) == 2 * getproperty(C, f)
+            end
+
+            # Update `U`.
+            C_new = ConstructionBase.setproperties(C, (U=2 * C.U,))
+            @test typeof(C_new) === typeof(C)
+            for f in propertynames(C)
+                @test getproperty(C_new, f) == 2 * getproperty(C, f)
+            end
+
+            # Update `UL`
+            C_new = ConstructionBase.setproperties(C, (UL=2 * C.UL,))
+            @test typeof(C_new) === typeof(C)
+            for f in propertynames(C)
+                @test getproperty(C_new, f) == 2 * getproperty(C, f)
+            end
+
+            # We can only set the properties with `LowerTriangular` or `UpperTriangular` matrices.
+            @test_throws ArgumentError ConstructionBase.setproperties(C, (L=parent(C.L),))
+            @test_throws ArgumentError ConstructionBase.setproperties(C, (U=parent(C.U),))
+            # Can only set one at the time.
+            @test_throws ArgumentError ConstructionBase.setproperties(C, (L=C.L, U=C.U,))
+            @test_throws ArgumentError ConstructionBase.setproperties(C, (UL=C.UL, U=C.U,))
+            @test_throws ArgumentError ConstructionBase.setproperties(C, (UL=C.UL, L=C.L,))
+            # And make sure any other patch will fail.
+            @test_throws ArgumentError ConstructionBase.setproperties(C, (asdf=C.UL,))
+        end
+    end
+
     @testset "Expr" begin
         e = :(a + b)
         @test e == @inferred constructorof(typeof(e))(getfields(e)...)