diff --git a/pandas/tests/frame/conftest.py b/pandas/tests/frame/conftest.py
index 486d140849159..05ceb2ded71d0 100644
--- a/pandas/tests/frame/conftest.py
+++ b/pandas/tests/frame/conftest.py
@@ -76,6 +76,11 @@ def bool_frame_with_na():
     # set some NAs
     df.iloc[5:10] = np.nan
     df.iloc[15:20, -2:] = np.nan
+
+    # For `any` tests we need to have at least one True before the first NaN
+    #  in each column
+    for i in range(4):
+        df.iloc[i, i] = True
     return df