diff --git a/public/client.js b/public/client.js
index f1af3a8f2..e3734901c 100644
--- a/public/client.js
+++ b/public/client.js
@@ -196,7 +196,8 @@ export function define(cell) {
   v.define(outputs.length ? `cell ${id}` : null, inputs, body);
   variables.push(v);
   for (const o of outputs) variables.push(main.define(o, [`cell ${id}`], (exports) => exports[o]));
-  for (const f of files) attachedFiles.set(f.name, {url: globalThis._FileAttachmentDir + `${(new URL(f.name, location)).pathname}`, mimeType: f.mimeType}); // prettier-ignore
+  const fadir = new URL(globalThis._FileAttachmentBase, location).href;
+  for (const f of files) attachedFiles.set(f.name, {url: new URL(f.name, fadir).pathname, mimeType: f.mimeType});
   for (const d of databases) databaseTokens.set(d.name, d);
 }
 
diff --git a/src/render.ts b/src/render.ts
index 374beefe6..d26327316 100644
--- a/src/render.ts
+++ b/src/render.ts
@@ -74,7 +74,7 @@ ${Array.from(getImportPreloads(parseResult, path))
 <script type="module">
 
 import {${preview ? "open, " : ""}define} from "${relativeUrl(path, "/_observablehq/client.js")}";
-globalThis._FileAttachmentDir = ${JSON.stringify(relativeUrl(path, "/_file/"))};
+globalThis._FileAttachmentBase = ${JSON.stringify(relativeUrl(path, "/_file" + dirname(path) + "/"))};
 
 ${preview ? `open({hash: ${JSON.stringify(hash)}});\n` : ""}${parseResult.cells
     .map(resolver)