diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 97c7898..696c2af 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -1,6 +1,6 @@
 repos:
   - repo: https://github.com/psf/black
-    rev: 20.8b1 # Replace by any tag/version: https://github.com/psf/black/tags
+    rev: 24.10.0 # Replace by any tag/version: https://github.com/psf/black/tags
     hooks:
       - id: black
         language_version: python3
diff --git a/src/mudata/_core/mudata.py b/src/mudata/_core/mudata.py
index a2cdf87..c77e85a 100644
--- a/src/mudata/_core/mudata.py
+++ b/src/mudata/_core/mudata.py
@@ -315,8 +315,12 @@ def _init_as_view(self, mudata_ref: "MuData", index):
 
         for attr, idx in (("obs", obsidx), ("var", varidx)):
             posmap = {}
+            size = getattr(self, attr).shape[0]
             for mod, mapping in getattr(mudata_ref, attr + "map").items():
-                posmap[mod] = mapping[idx].copy()
+                cposmap = np.zeros((size,), dtype=mapping.dtype)
+                cidx = mapping[idx] > 0
+                cposmap[cidx > 0] = np.arange(cidx.sum()) + 1
+                posmap[mod] = cposmap
             setattr(self, "_" + attr + "map", posmap)
 
         self.is_view = True
diff --git a/tests/test_view_copy.py b/tests/test_view_copy.py
index 41f3a31..819d60d 100644
--- a/tests/test_view_copy.py
+++ b/tests/test_view_copy.py
@@ -1,6 +1,7 @@
 from pathlib import Path
 
 import numpy as np
+import pandas as pd
 import pytest
 from anndata import AnnData
 
@@ -10,8 +11,15 @@
 
 @pytest.fixture()
 def mdata():
-    mod1 = AnnData(np.arange(0, 100, 0.1).reshape(-1, 10))
-    mod2 = AnnData(np.arange(101, 2101, 1).reshape(-1, 20))
+    rng = np.random.default_rng(42)
+    mod1 = AnnData(
+        np.arange(0, 100, 0.1).reshape(-1, 10),
+        obs=pd.DataFrame(index=rng.choice(150, size=100, replace=False)),
+    )
+    mod2 = AnnData(
+        np.arange(101, 2101, 1).reshape(-1, 20),
+        obs=pd.DataFrame(index=rng.choice(150, size=100, replace=False)),
+    )
     mods = {"mod1": mod1, "mod2": mod2}
     # Make var_names different in different modalities
     for m in ["mod1", "mod2"]:
@@ -70,6 +78,11 @@ def test_view_view(self, mdata):
         assert mdata_view.is_view
         assert mdata_view.n_obs == view_n_obs
 
+        for modname, mod in mdata_view.mod.items():
+            assert mdata_view.obsmap[modname].max() == mod.n_obs
+            idx = mdata_view.obsmap[modname]
+            assert np.all(mdata_view.obs_names[idx > 0] == mod.obs_names[idx[idx > 0] - 1])
+
         view_view_n_obs = 2
         mdata_view_view = mdata_view[list(range(view_view_n_obs)), :]
         assert mdata_view_view.is_view