diff --git a/__tests__/algorithm.test.ts b/__tests__/algorithm.test.ts
index 9025276..c8a3020 100644
--- a/__tests__/algorithm.test.ts
+++ b/__tests__/algorithm.test.ts
@@ -460,3 +460,53 @@ describe('change Params', () => {
     }).toThrow('Requested retention rate should be in the range (0,1]')
   })
 })
+
+describe('next_state', () => {
+  it('next_state not NaN', () => {
+    const f = fsrs()
+    const next_state = f.next_state(
+      { stability: 0, difficulty: 0 },
+      1,
+      1 /** Again */
+    )
+
+    expect(Number.isNaN(next_state.stability)).toBe(false)
+    expect(next_state).toEqual(f.next_state(null, 1, 1 /** Again */))
+    expect(next_state).toEqual(
+      f.next_state({ difficulty: 0, stability: 0 }, 1, 1 /** Again */)
+    )
+  })
+
+  it('invalid memory state', () => {
+    const f = fsrs()
+
+    const init = f.next_state(null, 0, 3 /** Good */)
+    // d<1
+    expect(() => {
+      f.next_state(
+        { stability: init.stability, difficulty: 0 },
+        1,
+        1 /** Again */
+      )
+    }).toThrow('invalid memory state')
+
+    // s<0.01
+    expect(() => {
+      f.next_state(
+        { stability: 0, difficulty: init.stability },
+        1,
+        1 /** Again */
+      )
+    }).toThrow('invalid memory state')
+
+    // g<0
+    expect(() => {
+      f.next_state(init, 1, -1 /** invalid grade */)
+    }).toThrow('invalid memory state')
+
+    // g>4
+    expect(() => {
+      f.next_state(init, 1, 5 /** invalid grade */)
+    }).toThrow('invalid memory state')
+  })
+})
diff --git a/src/fsrs/algorithm.ts b/src/fsrs/algorithm.ts
index 6f8ab13..75940f5 100644
--- a/src/fsrs/algorithm.ts
+++ b/src/fsrs/algorithm.ts
@@ -285,14 +285,20 @@ export class FSRSAlgorithm {
    * @returns The next state of memory with updated difficulty and stability.
    */
   next_state(memory_state: FSRSState | null, t: number, g: number): FSRSState {
-    if (!memory_state) {
+    const { difficulty: d, stability: s } = memory_state ?? {
+      difficulty: 0,
+      stability: 0,
+    }
+    if (d === 0 && s === 0) {
       return {
         difficulty: this.init_difficulty(clamp(g, 1, 4)),
         stability: this.init_stability(clamp(g, 1, 4)),
       }
     }
-    const { difficulty: d, stability: s } = memory_state
-    if (g < 1 || g > 4) {
+    if (d < 1 || s < 0.01 || g < 0 || g > 4) {
+      throw new Error('invalid memory state')
+    }
+    if (g === 0) {
       return {
         difficulty: d,
         stability: s,