diff --git a/src/earcut.js b/src/earcut.js
index 7136b61..aa1b733 100644
--- a/src/earcut.js
+++ b/src/earcut.js
@@ -933,7 +933,14 @@ export function refine(triangles, coords, dim = 2) {
         if (hStamp[h] !== gen) { hTable[h] = e; hStamp[h] = gen; } // first occurrence: insert
     }
 
-    while (i > 0) {
+    // Cap total flips: with non-robust inCircle, roundoff can make a quad and its flip both test
+    // as illegal, so a cascade can cycle forever (a legalized edge gets re-queued and flipped back).
+    // A converging cascade needs O(triangles) flips in practice, so a generous multiple of the
+    // half-edge count bounds legitimate work while breaking float-induced cycles; the worst case is
+    // then a few not-quite-Delaunay edges, never a hang.
+    let budget = 25 * n;
+
+    while (i > 0 && budget-- > 0) {
         const a = edgeStack[--i];
         edgeStamp[a] = 0;
         const b = he[a];
diff --git a/test/test.js b/test/test.js
index 69b2ccb..41c0ba0 100644
--- a/test/test.js
+++ b/test/test.js
@@ -187,6 +187,20 @@ test('refine preserves a concave polygon', () => {
     assert.equal(deviation(vertices, null, 2, triangles), 0);
 });
 
+test('refine terminates on near-cocircular points', {timeout: 5000}, () => {
+    const vertices = [
+        127.65906365022843, 9.336137742499535, 124.21725103117963, 30.888097161477972,
+        91.35514946628345, 89.65621376119454, 40.10446780041529, 121.5550560957686,
+        -110.83205604043928, 64.03323632184248, -127.20394987965459, -14.253249980770189,
+        61.074962259031416, -112.48932831632469, 127.37846573978545, -12.598669206638515,
+        127.77010311801033, -7.668164657400608];
+    const triangles = earcut(vertices);
+    const length = triangles.length;
+    refine(triangles, vertices);
+    assert.equal(triangles.length, length);
+    assert.ok(deviation(vertices, null, 2, triangles) < 1e-9);
+});
+
 test('refine legalizes all convex interior edges in earcut fixture', () => {
     const coords = JSON.parse(fs.readFileSync(new URL('fixtures/earcut.json', import.meta.url)));
     const data = flatten(coords);