diff --git a/src/triangular.jl b/src/triangular.jl
index b0af1c34..595a524d 100644
--- a/src/triangular.jl
+++ b/src/triangular.jl
@@ -623,7 +623,8 @@ end
     copytrito!(dest, U, U isa UpperOrUnitUpperTriangular ? 'L' : 'U')
     return dest
 end
-@propagate_inbounds function _copy!(dest::StridedMatrix, U::UpperOrLowerTriangular{<:Any, <:StridedMatrix})
+@propagate_inbounds function _copy!(dest::StridedMatrix,
+        U::Union{UnitUpperOrUnitLowerTriangular, UpperOrLowerTriangularStrided})
     U2 = Base.unalias(dest, U)
     copy_unaliased!(dest, U2)
     return dest
@@ -656,7 +657,7 @@ end
     end
     dest
 end
-@inline function copy_unaliased!(dest::StridedMatrix, U::UpperOrUnitUpperTriangular{<:Any, <:StridedMatrix})
+@inline function copy_unaliased!(dest::StridedMatrix, U::UpperOrUnitUpperTriangular)
     @boundscheck checkbounds(dest, axes(U)...)
     for col in axes(dest,2)
         @inbounds copy_unaliased_stored!(dest, U, col)
@@ -666,7 +667,7 @@ end
     end
     return dest
 end
-@inline function copy_unaliased!(dest::StridedMatrix, L::LowerOrUnitLowerTriangular{<:Any, <:StridedMatrix})
+@inline function copy_unaliased!(dest::StridedMatrix, L::LowerOrUnitLowerTriangular)
     @boundscheck checkbounds(dest, axes(L)...)
     for col in axes(dest,2)
         for row in firstindex(dest,1):col-1
diff --git a/test/triangular.jl b/test/triangular.jl
index c5dca32d..f7de5c10 100644
--- a/test/triangular.jl
+++ b/test/triangular.jl
@@ -6,6 +6,7 @@ isdefined(Main, :pruned_old_LA) || @eval Main include("prune_old_LA.jl")
 
 using Test, LinearAlgebra, Random
 using LinearAlgebra: errorbounds, transpose!, BandIndex
+using Test: GenericArray
 
 const BASE_TEST_PATH = joinpath(Sys.BINDIR, "..", "share", "julia", "test")
 
@@ -650,6 +651,16 @@ end
             @test_throws "cannot set index in the upper triangular part" copyto!(A, B)
         end
     end
+
+    @testset "partly initialized unit triangular" begin
+        for T in (UnitUpperTriangular, UnitLowerTriangular)
+            isupper = T == UnitUpperTriangular
+            M = Matrix{BigFloat}(undef, 2, 2)
+            M[1+!isupper,1+isupper] = 3
+            U = T(GenericArray(M))
+            @test copyto!(similar(M), U) == U
+        end
+    end
 end
 
 @testset "getindex with Integers" begin