Throughout this note let M be a differentiable manifold with an indefinite metric ( , ) of signature ( , .... + , . . . ) . For tangent vectors X, Y,... at any point, we shall use the following terminology. If ( X , X ) = ( Y , Y ) = I [resp. ( X , X ) = ( Y , Y)= 1 ] and (X, Y)=0, we say that the pair {X, Y} is orthonormal of signature (+ , +) [resp. ( , ) ] . If ( X , X ) = 1 , (Y, Y ) = I and (X, Y)=0, we say that {X, Y} is orthonormal of signature ( , +). Similarly, we speak of the signature of a nondegenerate 2-plane p of the tangent space as ( +, + ) or ( , + ) or ( , ) depending on the signature of the restriction of ( , ) to p. In Theorem 1 of [13, it was shown that the condition (*) (R(X, Y)Z,X)=0 whenever X, Y, Z are orthonormal vectors implies that all nondegenerate planes have the same sectional curvature. We shall make the following observations, which will be used later.