diff --git a/base/linalg/special.jl b/base/linalg/special.jl
index ccfd186b27f52..76e0d8f094cd4 100644
--- a/base/linalg/special.jl
+++ b/base/linalg/special.jl
@@ -7,13 +7,21 @@ convert{T}(::Type{Bidiagonal}, A::Diagonal{T})=Bidiagonal(A.diag, zeros(T, size(
 convert{T}(::Type{SymTridiagonal}, A::Diagonal{T})=SymTridiagonal(A.diag, zeros(T, size(A.diag,1)-1))
 convert{T}(::Type{Tridiagonal}, A::Diagonal{T})=Tridiagonal(zeros(T, size(A.diag,1)-1), A.diag, zeros(T, size(A.diag,1)-1))
 convert(::Type{UpperTriangular}, A::Diagonal) = UpperTriangular(full(A), :L)
-convert(::Type{UnitUpperTriangular}, A::Diagonal) = UnitUpperTriangular(full(A), :L)
 convert(::Type{LowerTriangular}, A::Diagonal) = LowerTriangular(full(A), :L)
-convert(::Type{UnitLowerTriangular}, A::Diagonal) = UnitLowerTriangular(full(A), :L)
 convert(::Type{LowerTriangular}, A::Bidiagonal) = !A.isupper ? LowerTriangular(full(A)) : throw(ArgumentError("Bidiagonal matrix must have lower off diagonal to be converted to LowerTriangular"))
 convert(::Type{UpperTriangular}, A::Bidiagonal) = A.isupper ? UpperTriangular(full(A)) : throw(ArgumentError("Bidiagonal matrix must have upper off diagonal to be converted to UpperTriangular"))
 convert(::Type{Matrix}, D::Diagonal) = diagm(D.diag)
 
+function convert(::Type{UnitUpperTriangular}, A::Diagonal)
+    all(A.diag .== one(eltype(A))) || throw(ArgumentError("Matrix cannot be represented as UnitUpperTriangular"))
+    UnitUpperTriangular(full(A))
+end
+
+function convert(::Type{UnitLowerTriangular}, A::Diagonal)
+    all(A.diag .== one(eltype(A))) || throw(ArgumentError("Matrix cannot be represented as UnitLowerTriangular"))
+    UnitLowerTriangular(full(A))
+end
+
 function convert(::Type{Diagonal}, A::Union(Bidiagonal, SymTridiagonal))
     all(A.ev .== 0) || throw(ArgumentError("Matrix cannot be represented as Diagonal"))
     Diagonal(A.dv)
diff --git a/test/linalg4.jl b/test/linalg4.jl
index e7c2e14650f02..cf3995a4e7b4c 100644
--- a/test/linalg4.jl
+++ b/test/linalg4.jl
@@ -13,6 +13,10 @@ let a=[1.0:n;]
         debug && println("newtype is $(newtype)")
         @test full(convert(newtype, A)) == full(A)
     end
+    for newtype in [Base.LinAlg.UnitUpperTriangular, Base.LinAlg.UnitLowerTriangular]
+        @test_throws ArgumentError convert(newtype, A)
+        @test full(convert(newtype, Diagonal(ones(n)))) == eye(n)
+    end
 
     for isupper in (true, false)
         debug && println("isupper is $(isupper)")
@@ -38,6 +42,8 @@ let a=[1.0:n;]
     for newtype in [Diagonal, Bidiagonal]
         @test_throws ArgumentError convert(newtype,A)
     end
+    A = SymTridiagonal(a, zeros(n-1))
+    @test full(convert(Bidiagonal,A)) == full(A)
 
     A = Tridiagonal(zeros(n-1), [1.0:n;], zeros(n-1)) #morally Diagonal
     for newtype in [Diagonal, Bidiagonal, SymTridiagonal, Matrix]