diff --git a/base/utf16.jl b/base/utf16.jl
index 8caa3fd14f19d..134e8b8ddaaf7 100644
--- a/base/utf16.jl
+++ b/base/utf16.jl
@@ -143,3 +143,28 @@ function utf16(p::Union{Ptr{UInt16}, Ptr{Int16}})
     while unsafe_load(p, len+1) != 0; len += 1; end
     utf16(p, len)
 end
+
+function map(fun, str::UTF16String)
+    buf = UInt16[]
+    sizehint!(buf, length(str.data))
+    for ch in str
+        c2 = fun(ch)
+        if !isa(c2, Char)
+            throw(UnicodeError(UTF_ERR_MAP_CHAR, 0, 0))
+        end
+        uc = reinterpret(UInt32, c2)
+        if uc < 0x10000
+            if utf16_is_surrogate(UInt16(uc))
+                throw(UnicodeError(UTF_ERR_INVALID_CHAR, 0, uc))
+            end
+            push!(buf, UInt16(uc))
+        elseif uc <= 0x10ffff
+            push!(buf, UInt16(0xd7c0 + (uc >> 10)))
+            push!(buf, UInt16(0xdc00 + (uc & 0x3ff)))
+        else
+            throw(UnicodeError(UTF_ERR_INVALID_CHAR, 0, uc))
+        end
+    end
+    push!(buf, 0)
+    UTF16String(buf)
+end
diff --git a/test/strings.jl b/test/strings.jl
index 3701567bae68e..855634722e0b6 100644
--- a/test/strings.jl
+++ b/test/strings.jl
@@ -1897,3 +1897,23 @@ end
 @test [c for c in "ḟøøƀäṙ"] == ['ḟ', 'ø', 'ø', 'ƀ', 'ä', 'ṙ']
 @test [i for i in eachindex("ḟøøƀäṙ")] == [1, 4, 6, 8, 10, 12]
 @test [x for x in enumerate("ḟøøƀäṙ")] == [(1, 'ḟ'), (2, 'ø'), (3, 'ø'), (4, 'ƀ'), (5, 'ä'), (6, 'ṙ')]
+
+# issue # 11464: uppercase/lowercase of UTF16String becomes a UTF8String
+str = "abcdef\uff\uffff\u10ffffABCDEF"
+@test typeof(uppercase("abcdef")) == ASCIIString
+@test typeof(uppercase(utf8(str))) == UTF8String
+@test typeof(uppercase(utf16(str))) == UTF16String
+@test typeof(uppercase(utf32(str))) == UTF32String
+@test typeof(lowercase("ABCDEF")) == ASCIIString
+@test typeof(lowercase(utf8(str))) == UTF8String
+@test typeof(lowercase(utf16(str))) == UTF16String
+@test typeof(lowercase(utf32(str))) == UTF32String
+
+foomap(ch) = (ch > 65)
+foobar(ch) = Char(0xd800)
+foobaz(ch) = Char(0x200000)
+@test_throws UnicodeError map(foomap, utf16(str))
+@test_throws UnicodeError map(foobar, utf16(str))
+@test_throws UnicodeError map(foobaz, utf16(str))
+
+