diff --git a/README.md b/README.md
index 795133b..71da83e 100644
--- a/README.md
+++ b/README.md
@@ -58,12 +58,12 @@ A::StridedMatrix{R} where {R <: Real} == Z * T * transpose(Z)
 where `T` is quasi-upper-triangular and `Z` is orthogonal, both with the
 same element type as `A`.  This is what you get by invoking the above-mentioned
 functions with matrix arguments whose element type `T <: Real`.
-By default, the result is not quite in standard form, in that some
-pair-blocks (and therefore rank-2 invariant subspaces) are not fully resolved.
+By default, the result is in standard form, so
+pair-blocks (and therefore rank-2 invariant subspaces) should be fully resolved.
+(This differs from the original version in GenericLinearAlgebra.jl.)
 
-If the optional keyword `standardized` is set to `true` in `gschur`, a
-standard form is produced.  There are currently a few cases where this
-does not give a correct decomposition (a problem under study).
+If the optional keyword `standardized` is set to `false` in `gschur`, a
+non-standard (but less expensive) form is produced.
 
 Eigenvectors are not currently available for the "real Schur" forms.