diff --git a/src/symmetric.jl b/src/symmetric.jl
index 98f3429d..09819325 100644
--- a/src/symmetric.jl
+++ b/src/symmetric.jl
@@ -441,6 +441,10 @@ issymmetric(A::Hermitian{<:Real}) = true
 issymmetric(A::Hermitian{<:Complex}) = isreal(A)
 issymmetric(A::Symmetric) = true
 
+# check if the symmetry is known from the type
+_issymmetric(::Union{SymSymTri, Hermitian{<:Real}}) = true
+_issymmetric(::Any) = false
+
 adjoint(A::Hermitian) = A
 transpose(A::Symmetric) = A
 adjoint(A::Symmetric{<:Real}) = A
diff --git a/src/tridiag.jl b/src/tridiag.jl
index 10c43a2b..226b9417 100644
--- a/src/tridiag.jl
+++ b/src/tridiag.jl
@@ -111,16 +111,14 @@ function (::Type{SymTri})(A::AbstractMatrix) where {SymTri <: SymTridiagonal}
     checksquare(A)
     du = diag(A, 1)
     d  = diag(A)
-    dl = diag(A, -1)
-    if _checksymmetric(d, du, dl)
-        SymTri(d, du)
-    else
+    if !(_issymmetric(A) || _checksymmetric(d, du, diag(A, -1)))
         throw(ArgumentError("matrix is not symmetric; cannot convert to SymTridiagonal"))
     end
+    return SymTri(d, du)
 end
 
 _checksymmetric(d, du, dl) = all(((x, y),) -> x == transpose(y), zip(du, dl)) && all(issymmetric, d)
-_checksymmetric(A::AbstractMatrix) = _checksymmetric(diagview(A), diagview(A, 1), diagview(A, -1))
+_checksymmetric(A::AbstractMatrix) = _issymmetric(A) || _checksymmetric(diagview(A), diagview(A, 1), diagview(A, -1))
 
 SymTridiagonal{T,V}(S::SymTridiagonal{T,V}) where {T,V<:AbstractVector{T}} = S
 SymTridiagonal{T,V}(S::SymTridiagonal) where {T,V<:AbstractVector{T}} =
diff --git a/test/tridiag.jl b/test/tridiag.jl
index f44df3f7..849dfa17 100644
--- a/test/tridiag.jl
+++ b/test/tridiag.jl
@@ -1172,4 +1172,16 @@ end
     end
 end
 
+@testset "SymTridiagonal from Symmetric" begin
+    S = Symmetric(reshape(1:9, 3, 3))
+    @testset "helper functions" begin
+        @test LinearAlgebra._issymmetric(S)
+        @test !LinearAlgebra._issymmetric(Array(S))
+    end
+    ST = SymTridiagonal(S)
+    @test ST == SymTridiagonal(diag(S), diag(S,1))
+    S = Symmetric(Tridiagonal(1:3, 1:4, 1:3))
+    @test convert(SymTridiagonal, S) == S
+end
+
 end # module TestTridiagonal