diff --git a/NEWS.md b/NEWS.md
index 06fc108cd..fe05e190c 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -90,7 +90,7 @@
 
 6. In `DT[,j,by]`, `by` retains its attributes (e.g. class) when `j` is GForce optimized, [#5567](https://github.com/Rdatatable/data.table/issues/5567). Thanks to @danwwilson for the report, and @ben-schwen for the PR.
 
-7. `dt[,,by=año]` (i.e., using a column name containing a non-ASCII character in `by` as a plain symbol) no longer errors with "object 'año' not found", #4708. Thanks @pfv07 for the report, and @MichaelChirico for the fix.
+7. `dt[,,by=año]` (i.e., using a column name containing a non-ASCII character in `by` as a plain symbol) no longer errors with "object 'año' not found", #4708. Thanks @pfv07 for the report, and @MichaelChirico for the fix. Also thanks to @aitap for suggesting an improvement to the corresponding test.
 
 8. Fixed some memory management issues in the C routines backing `melt()`, `froll()`, and GForce `mean()`, as identified by `rchk`. Thanks Tomas Kalibera and the CRAN team for setting up the `rchk` system, and @MichaelChirico for the fix.
 
diff --git a/inst/tests/tests.Rraw b/inst/tests/tests.Rraw
index 804002f0a..581d5395e 100644
--- a/inst/tests/tests.Rraw
+++ b/inst/tests/tests.Rraw
@@ -18724,16 +18724,19 @@ if (test_bit64) local({
 })
 
 # non-ASCII plain symbol in by, #4708
-DT = data.table(a = rep(1:3, 2))
-# NB: recall we can't use non-ASCII symbols here. the text is a-<n-tilde>-o (year in Spanish)
-setnames(DT, "a", "a\U00F1o")
-test(2266, eval(parse(text="DT[ , .N, a\U00F1o]$N[1L]")), 2L)
-# sub-key can also be retained in plain query, part of #4498
-DT = data.table(id = rep(1:10, 2L), grp = rep(1:2, each=10L), V = 1:20/13, key=c('id', 'grp'))
-test(2266.1, key(DT[ , .(id)]), 'id')
-test(2266.2, key(DT[ , .(grp)]), NULL)
-## renaming also caught
-test(2266.3, key(DT[ , .(newid = id, newgrp = grp)]), c('newid', 'newgrp'))
+native_ano = iconv("a\U00F1o", "UTF-8", "")
+if (!is.na(native_ano)) { # #6339: symbol must be represented in native encoding
+  DT = data.table(a = rep(1:3, 2))
+  # NB: recall we can't use non-ASCII symbols here. the text is a-<n-tilde>-o (year in Spanish)
+  setnames(DT, "a", native_ano)
+  test(2266, eval(parse(text=sprintf("DT[ , .N, %s]$N[1L]", native_ano))), 2L)
+  # sub-key can also be retained in plain query, part of #4498
+  DT = data.table(id = rep(1:10, 2L), grp = rep(1:2, each=10L), V = 1:20/13, key=c('id', 'grp'))
+  test(2266.1, key(DT[ , .(id)]), 'id')
+  test(2266.2, key(DT[ , .(grp)]), NULL)
+  ## renaming also caught
+  test(2266.3, key(DT[ , .(newid = id, newgrp = grp)]), c('newid', 'newgrp'))
+}
 
 # all.equal failed to dispatch to methods of columns, #4543
 DT1 = data.table(t = .POSIXct(1590973200, tz='UTC'))