diff --git a/packages/router/__tests__/location.spec.ts b/packages/router/__tests__/location.spec.ts
index 0511ad89f..7b7497687 100644
--- a/packages/router/__tests__/location.spec.ts
+++ b/packages/router/__tests__/location.spec.ts
@@ -156,12 +156,24 @@ describe('parseURL', () => {
       hash: '#hash',
       query: {},
     })
+    expect(parseURL('/foo#hash')).toEqual({
+      fullPath: '/foo#hash',
+      path: '/foo',
+      hash: '#hash',
+      query: {},
+    })
     expect(parseURL('/foo?')).toEqual({
       fullPath: '/foo?',
       path: '/foo',
       hash: '',
       query: {},
     })
+    expect(parseURL('/foo')).toEqual({
+      fullPath: '/foo',
+      path: '/foo',
+      hash: '',
+      query: {},
+    })
   })
 
   it('works with empty hash', () => {
@@ -177,6 +189,12 @@ describe('parseURL', () => {
       hash: '#',
       query: {},
     })
+    expect(parseURL('/foo')).toEqual({
+      fullPath: '/foo',
+      path: '/foo',
+      hash: '',
+      query: {},
+    })
   })
 
   it('works with a relative paths', () => {
@@ -198,7 +216,20 @@ describe('parseURL', () => {
       hash: '',
       query: {},
     })
+    // cannot go below root
+    expect(parseURL('../../foo', '/parent/bar')).toEqual({
+      fullPath: '/foo',
+      path: '/foo',
+      hash: '',
+      query: {},
+    })
 
+    expect(parseURL('', '/parent/bar')).toEqual({
+      fullPath: '/parent/bar',
+      path: '/parent/bar',
+      hash: '',
+      query: {},
+    })
     expect(parseURL('#foo', '/parent/bar')).toEqual({
       fullPath: '/parent/bar#foo',
       path: '/parent/bar',